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LIPIcs, Volume 359
36th International Symposium on Algorithms and Computation (ISAAC 2025)
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Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Symposium on Algorithms and Computation (ISAAC)
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- published at: 2025-11-27
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-408-6
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Complete Volume
LIPIcs, Volume 359, ISAAC 2025, Complete Volume
Abstract
LIPIcs, Volume 359, ISAAC 2025, Complete Volume
Cite as
36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 1-962, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@Proceedings{chen_et_al:LIPIcs.ISAAC.2025,
title = {{LIPIcs, Volume 359, ISAAC 2025, Complete Volume}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {1--962},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025},
URN = {urn:nbn:de:0030-drops-250773},
doi = {10.4230/LIPIcs.ISAAC.2025},
annote = {Keywords: LIPIcs, Volume 359, ISAAC 2025, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{chen_et_al:LIPIcs.ISAAC.2025.0,
author = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {0:i--0:xvi},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.0},
URN = {urn:nbn:de:0030-drops-250760},
doi = {10.4230/LIPIcs.ISAAC.2025.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
Challenges and Opportunities of Graph-Based Algorithms for Similarity Search (Invited Talk)
Abstract
Over the last few years, graph-based approaches to nearest neighbor search have attracted renewed interest. Algorithms such as HNSW, NSG, and DiskANN have become popular tools in practice. These algorithms are highly versatile and come with efficient implementations. At the same time, their correctness, performance guarantees, and functionality remain poorly understood. In this talk, I will discuss the challenges and opportunities presented by this class of algorithms.
Cite as
Piotr Indyk. Challenges and Opportunities of Graph-Based Algorithms for Similarity Search (Invited Talk). In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{indyk:LIPIcs.ISAAC.2025.1,
author = {Indyk, Piotr},
title = {{Challenges and Opportunities of Graph-Based Algorithms for Similarity Search}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {1:1--1:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.1},
URN = {urn:nbn:de:0030-drops-249092},
doi = {10.4230/LIPIcs.ISAAC.2025.1},
annote = {Keywords: Similarity search}
}
Document
Invited Talk
Hash Functions Bridging the Gap from Theory to Practice (Invited Talk)
Abstract
Randomized algorithms are often enjoyed for their simplicity, but the hash functions employed to yield the desired probabilistic guarantees are often too complicated to be practical. Hash functions are used everywhere in computing, e.g., hash tables, sketching, dimensionality reduction, sampling, and estimation. Many of these applications are relevant to Machine Learning, where we are often interested in similarity between high dimensional objects. Reducing the dimensionality is key to efficient processing. Abstractly, we like to think of hashing as fully-random hashing, assigning independent hash values to every possible key, but essentially this requires us to store the hash values for all keys, which is unrealistic for most key universes, e.g., 64-bit keys. In practice we have to settle for implementable hash functions, and often practitioners settle for implementations that are too simple in that the algorithms end up working only for sufficiently random input. However, the real world is full of structured/non-random input. The issue is severe, for simplistic hash functions will often work very well in tests with random input. Moreover, the issue is often that error events that should never happen in practice, happen with way too high probability. This does not show in a few tests, but will show up over time when you put the system into production. Over the last decade there has been major developments in simple to implement tabulation based hash functions offering strong theoretical guarantees, so as to support fundamental properties such as Chernoff bounds, Sparse Johnson-Lindenstrauss transforms, and fully-random hashing on a given set w.h.p. etc. I will discuss some of the principles of these developments and offer insights on how far we can bridge from theory (assuming fully-random hash functions) to practice (needing something that can actually implemented efficiently).
Cite as
Mikkel Thorup. Hash Functions Bridging the Gap from Theory to Practice (Invited Talk). In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{thorup:LIPIcs.ISAAC.2025.2,
author = {Thorup, Mikkel},
title = {{Hash Functions Bridging the Gap from Theory to Practice}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {2:1--2:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.2},
URN = {urn:nbn:de:0030-drops-249102},
doi = {10.4230/LIPIcs.ISAAC.2025.2},
annote = {Keywords: Hash functions}
}
Document
Circle-Segment Intersection Queries in Connected Geometric Graphs
Abstract
In this paper, we study the problem of efficiently reporting all intersections between a given set of line segments in the plane and a query circle, focusing on the case where the segments form the edges of a connected geometric graph. While previous data structures for circle-segment intersection queries on general segment sets incur high space or query time costs, we exploit the connectivity of the input to obtain significantly improved performance. In fact, we propose a new circle-segment intersection data structure that can be constructed in 𝒪((n + C) log³ n) time and space on connected graphs with n edges and C edge crossings. It answers intersection queries in 𝒪(k log³ n) time, where k denotes the output size. Our method relies on the construction of efficient circle-graph intersection oracles as well as a novel linear-time algorithm to partition the edges of the graph into balanced, connected components, which might be of independent interest. In a proof-of-concept experimental study on real-world road networks, we show that our novel data structure also performs well in practice. Even on networks with millions of edges, the construction time is within minutes and queries are answered in a few milliseconds.
Cite as
Peyman Afshani, Yannick Bosch, and Sabine Storandt. Circle-Segment Intersection Queries in Connected Geometric Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{afshani_et_al:LIPIcs.ISAAC.2025.3,
author = {Afshani, Peyman and Bosch, Yannick and Storandt, Sabine},
title = {{Circle-Segment Intersection Queries in Connected Geometric Graphs}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {3:1--3:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.3},
URN = {urn:nbn:de:0030-drops-249114},
doi = {10.4230/LIPIcs.ISAAC.2025.3},
annote = {Keywords: Intersection data structure, Graph partitioning, Dobkin-Kirkpatrick hierarchy}
}
Document
Finding d-Cuts in Claw-Free Graphs
Abstract
The Matching Cut problem is to decide if the vertex set of a connected graph can be partitioned into two non-empty sets B and R such that the edges between B and R form a matching, that is, every vertex in B has at most one neighbour in R, and vice versa. If for some integer d ≥ 1, we allow every vertex in B to have at most d neighbours in R, and vice versa, we obtain the more general problem d-Cut. It is known that d-Cut is NP-complete for every d ≥ 1. However, for claw-free graphs, it is only known that d-Cut is polynomial-time solvable for d = 1 and NP-complete for d ≥ 3. We resolve the missing case d = 2 by proving NP-completeness. This follows from our more general study, in which we also bound the maximum degree. That is, we prove that for every d ≥ 2, d-Cut, restricted to claw-free graphs of maximum degree p, is constant-time solvable if p ≤ 2d+1 and NP-complete if p ≥ 2d+3. Moreover, in the former case, we can find a d-cut in linear time. We also show how our positive results for claw-free graphs can be generalized to S_{1^t,𝓁}-free graphs where S_{1^t,𝓁} is the graph obtained from a star on t+2 vertices by subdividing one of its edges exactly 𝓁 times.
Cite as
Jungho Ahn, Tala Eagling-Vose, Felicia Lucke, Daniël Paulusma, and Siani Smith. Finding d-Cuts in Claw-Free Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{ahn_et_al:LIPIcs.ISAAC.2025.4,
author = {Ahn, Jungho and Eagling-Vose, Tala and Lucke, Felicia and Paulusma, Dani\"{e}l and Smith, Siani},
title = {{Finding d-Cuts in Claw-Free Graphs}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {4:1--4:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.4},
URN = {urn:nbn:de:0030-drops-249121},
doi = {10.4230/LIPIcs.ISAAC.2025.4},
annote = {Keywords: matching cut, d-cut, claw-free, maximum degree}
}
Document
Graph Coloring Below Guarantees via Co-Triangle Packing
Abstract
In the 𝓁-Coloring problem, we are given a graph on n nodes, and tasked with determining if its vertices can be properly colored using 𝓁 colors. In this paper we study below-guarantee graph coloring, which tests whether an n-vertex graph can be properly colored using g-k colors, where g is a trivial upper bound such as n. We introduce an algorithmic framework that builds on a packing of co-triangles K₃ (independent sets of three vertices): the algorithm greedily finds co-triangles and employs a win-win analysis. If many are found, we immediately return yes; otherwise these co-triangles form a small co-triangle modulator, whose deletion makes the graph co-triangle-free.
Extending the work of [Gutin et al., SIDMA 2021], who solved 𝓁-Coloring (for any 𝓁) in randomized O^∗(2^k) time when given a K₂-free modulator of size k, we show that this problem can likewise be solved in randomized O^*(2^{k}) time when given a K₃-free modulator of size k.
This result in turn yields a randomized O^*(2^{3k/2}) algorithm for (n-k)-Coloring (also known as Dual Coloring), improving the previous O^*(4^k) bound. We then introduce a smaller parameterization, (ω+μ-k)-Coloring, where ω is the clique number and μ is the size of a maximum matching in the complement graph; since ω+μ ≤ n for any graph, this problem is strictly harder. Using the same co-triangle-packing argument, we obtain a randomized O^*(2^{6k}) algorithm, establishing its fixed-parameter tractability for a smaller parameter. Complementing this finding, we show that no fixed-parameter tractable algorithm exists for (ω-k)-Coloring or (μ-k)-Coloring under standard complexity assumptions.
Cite as
Shyan Akmal and Tomohiro Koana. Graph Coloring Below Guarantees via Co-Triangle Packing. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{akmal_et_al:LIPIcs.ISAAC.2025.5,
author = {Akmal, Shyan and Koana, Tomohiro},
title = {{Graph Coloring Below Guarantees via Co-Triangle Packing}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {5:1--5:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.5},
URN = {urn:nbn:de:0030-drops-249130},
doi = {10.4230/LIPIcs.ISAAC.2025.5},
annote = {Keywords: coloring, parameterized algorithms, algebraic algorithms, above-guarantee, below-guarantee, subset convolution, determinants}
}
Document
A Dimension-Reducing Fréchet Simplification Oracle
Abstract
Let P be a polygonal curve with n vertices in the plane. We construct a data structure of size O(n log n) suited for simplification queries of the following kind. Given a query line 𝓁 and an integer k ≥ 1, find a curve Q on 𝓁 with at most k vertices that minimizes the discrete Fréchet distance to P, among all such curves. Using our data structure, a query can be handled in O(k² log³ n + k log⁴n) time.
More generally, a geometric tree T on n vertices in the plane can be preprocessed into a near-linear-size structure so that, given a pair u, v of its vertices, a line 𝓁, and an integer k ≥ 1, one can find a curve Q on 𝓁 with at most k vertices that minimizes the discrete Fréchet distance to the path from u to v in T, in time O(k² polylog n).
For the general dimension-reduction problem, where P is a curve in ℝ^d (d ≥ 3), 0 < ε₀ < 1 is a real parameter, and a query specifies a g-flat h (1 ≤ g ≤ d-1) and an integer k ≥ 1, we construct a data structure of size O(nlog n + f(ε₀) n), where f(ε₀) = (1+1/ε₀)^{(d-1)/2}, that allows us to find a curve Q on h with at most k vertices, whose discrete Fréchet distance to P is at most 1+ε₀ times the distance of Q^* to P, where Q^* is such a curve that minimizes the distance to P. The query handling time is O(f(ε₀) k² log² n).
Cite as
Boris Aronov, Tsuri Farhana, Matthew J. Katz, and Indu Ramesh. A Dimension-Reducing Fréchet Simplification Oracle. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{aronov_et_al:LIPIcs.ISAAC.2025.6,
author = {Aronov, Boris and Farhana, Tsuri and Katz, Matthew J. and Ramesh, Indu},
title = {{A Dimension-Reducing Fr\'{e}chet Simplification Oracle}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {6:1--6:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.6},
URN = {urn:nbn:de:0030-drops-249149},
doi = {10.4230/LIPIcs.ISAAC.2025.6},
annote = {Keywords: Computational geometry, discrete Fr\'{e}chet distance, curve simplification oracle, restricted minimum enclosing disk queries}
}
Document
Polynomial Equivalence of Extended Chemical Reaction Models
Abstract
The ability to detect whether a species (or dimension) is zero in Chemical Reaction Networks (CRN), Vector Addition Systems, or Petri Nets is known to increase the power of these models - making them capable of universal computation. While this ability may appear in many forms, such as extending the models to allow transitions to be inhibited, prioritized, or synchronized, we present an extension that directly performs this zero checking. We introduce a new void genesis CRN variant with a simple design that merely increments the count of a specific species when any other species' count goes to zero. As with previous extensions, we show that the model is Turing Universal. We then analyze several other studied CRN variants and show that they are all equivalent through a polynomial simulation with the void genesis model, which does not merely follow from Turing-universality. Thus, inhibitor species, reactions that occur at different rates, being allowed to run reactions in parallel, or even being allowed to continually add more volume to the CRN, does not add additional simulation power beyond simply detecting if a species count becomes zero.
Cite as
Divya Bajaj, Jose-Luis Castellanos, Ryan Knobel, Austin Luchsinger, Aiden Massie, Adrian Salinas, Pablo Santos, Ramiro Santos, Robert Schweller, and Tim Wylie. Polynomial Equivalence of Extended Chemical Reaction Models. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bajaj_et_al:LIPIcs.ISAAC.2025.7,
author = {Bajaj, Divya and Castellanos, Jose-Luis and Knobel, Ryan and Luchsinger, Austin and Massie, Aiden and Salinas, Adrian and Santos, Pablo and Santos, Ramiro and Schweller, Robert and Wylie, Tim},
title = {{Polynomial Equivalence of Extended Chemical Reaction Models}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {7:1--7:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.7},
URN = {urn:nbn:de:0030-drops-249158},
doi = {10.4230/LIPIcs.ISAAC.2025.7},
annote = {Keywords: Chemical Reaction Networks, Simulations, Petri-nets, Vector Addition Systems, Bi-simulation, Turing-universality, Inhibitors}
}
Document
Parameterized Algorithms for the Drone Delivery Problem
Abstract
Timely delivery and optimal routing remain fundamental challenges in the modern logistics industry. Building on prior work that considers single-package delivery across networks using multiple types of collaborative agents with restricted movement areas (e.g., drones or trucks), we examine the complexity of the problem under structural and operational constraints. Our focus is on minimizing total delivery time by coordinating agents that differ in speed and movement range across a graph. This problem formulation aligns with the recently proposed Drone Delivery Problem with respect to delivery time (DDT), introduced by Erlebach et al. [ISAAC 2022].
We first resolve an open question posed by Erlebach et al. [ISAAC 2022] by showing that even when the delivery network is a path graph, DDT admits no polynomial-time approximation within any polynomially encodable factor a(n), unless P=NP. Additionally, we identify the intersection graph of the agents, where nodes represent agents and edges indicate an overlap of the movement areas of two agents, as an important structural concept. For path graphs, we show that DDT becomes tractable when parameterized by the treewidth w of the intersection graph, and we present an exact FPT algorithm with running time f(w)⋅poly(n,k), for some computable function f. For general graphs, we give an FPT algorithm with running time f(Δ,w)⋅poly(n,k), where Δ is the maximum degree of the intersection graph. In the special case where the intersection graph is a tree, we provide a simple polynomial-time algorithm.
Cite as
Simon Bartlmae, Andreas Hene, Joshua Könen, and Heiko Röglin. Parameterized Algorithms for the Drone Delivery Problem. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bartlmae_et_al:LIPIcs.ISAAC.2025.8,
author = {Bartlmae, Simon and Hene, Andreas and K\"{o}nen, Joshua and R\"{o}glin, Heiko},
title = {{Parameterized Algorithms for the Drone Delivery Problem}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {8:1--8:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.8},
URN = {urn:nbn:de:0030-drops-249162},
doi = {10.4230/LIPIcs.ISAAC.2025.8},
annote = {Keywords: Complexity, Delivery, FPT algorithms, Graph Theory}
}
Document
Small Space Encoding and Recognition of k-Palindromic Prefixes
Abstract
Palindromes are non-empty strings that read the same forward and backward. We study the problem of recognizing so-called k-palindromic strings, which can be represented as the concatenation of exactly k palindromes. [Rubinchik and Shur, MFCS 2020] showed that the problem is solvable in linear space and time. We present a read-only algorithm that recognizes all k-palindromic prefixes of a string T of length n in O(n ⋅ 6^{k²} ⋅ log^k n) time and O(6^{k²} ⋅ log^k n) space. As a corollary, we also obtain a read-only algorithm for computing the palindromic length of T, i.e., the smallest k such that T is k-palindromic, in O(n ⋅ 6^{k²} ⋅ log^⌈k/2⌉ n) time and O(6^{k²} ⋅ log^⌈k/2⌉ n) space.
Cite as
Gabriel Bathie, Jonas Ellert, and Tatiana Starikovskaya. Small Space Encoding and Recognition of k-Palindromic Prefixes. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bathie_et_al:LIPIcs.ISAAC.2025.9,
author = {Bathie, Gabriel and Ellert, Jonas and Starikovskaya, Tatiana},
title = {{Small Space Encoding and Recognition of k-Palindromic Prefixes}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {9:1--9:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.9},
URN = {urn:nbn:de:0030-drops-249178},
doi = {10.4230/LIPIcs.ISAAC.2025.9},
annote = {Keywords: palindromic length, read-only algorithms, palindromes}
}
Document
New Algorithmic Directions in Optimal Transport and Applications for Product Spaces
Abstract
We consider the problem of optimal transport between two high-dimensional distributions μ,ν in ℝⁿ from a new algorithmic perspective, in which we are given a sample x ∼ μ and we have to find a close y ∼ ν while running in poly(n) time, where n is the size/dimension of x,y. In other words, we are interested in making the running time bounded in dimension of the spaces rather than bounded in the total size of the representations of the two distributions. Our main result is a general algorithmic transport result between any product distribution μ and an arbitrary distribution ν of total cost Δ + δ under 𝓁_p^p cost; here Δ is the cost of the so-called Knothe–Rosenblatt transport from μ to ν, while δ is a computational error that goes to zero for larger running time in the transport algorithm. For this result, we need ν to be "sequentially samplable" with a "bounded average sampling cost" which is a novel but natural notion of independent interest. In addition, we prove the following.
- We prove an algorithmic version of the celebrated Talagrand’s inequality for transporting the standard Gaussian distribution Φⁿ to an arbitrary ν under the Euclidean-squared cost. When ν is Φⁿ conditioned on a set S of measure ε, we show how to implement the needed sequential sampler for ν in expected time poly(n/ε), using membership oracle access to S. Hence, we obtain an algorithmic transport that maps Φⁿ to Φⁿ|S in time poly(n/ε) and expected Euclidean-squared distance O(log 1/ε), which is optimal for a general set S of measure ε.
- As corollary, we find the first computational concentration (Etesami et al. SODA 2020) result for the Gaussian measure under the Euclidean distance with a dimension-independent transportation cost, resolving a question of Etesami et al. More precisely, for any set S of Gaussian measure ε, we map most of Φⁿ samples to S with Euclidean distance O(√{log 1/ε}) in time poly(n/ε).
Cite as
Salman Beigi, Omid Etesami, Mohammad Mahmoody, and Amir Najafi. New Algorithmic Directions in Optimal Transport and Applications for Product Spaces. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{beigi_et_al:LIPIcs.ISAAC.2025.10,
author = {Beigi, Salman and Etesami, Omid and Mahmoody, Mohammad and Najafi, Amir},
title = {{New Algorithmic Directions in Optimal Transport and Applications for Product Spaces}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {10:1--10:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.10},
URN = {urn:nbn:de:0030-drops-249187},
doi = {10.4230/LIPIcs.ISAAC.2025.10},
annote = {Keywords: Optimal transport, Randomized algorithms, Concentration bounds}
}
Document
Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure
Abstract
We generalize the polynomial-time solvability of k-Diverse Minimum s-t Cuts (De Berg et al., ISAAC'23) to a wider class of combinatorial problems whose solution sets have a distributive lattice structure. We identify three structural conditions that, when met by a problem, ensure that a k-sized multiset of maximally-diverse solutions - measured by the sum of pairwise Hamming distances - can be found in polynomial time. We apply this framework to obtain polynomial-time algorithms for finding diverse minimum s-t cuts, diverse stable matchings, and diverse market-clearing price vectors. Moreover, we show that the framework extends to two other natural measures of diversity. Lastly, we present a simpler algorithmic framework for finding a largest set of pairwise disjoint solutions in problems that meet these structural conditions.
Cite as
Mark de Berg, Andrés López Martínez, and Frits Spieksma. Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{deberg_et_al:LIPIcs.ISAAC.2025.11,
author = {de Berg, Mark and L\'{o}pez Mart{\'\i}nez, Andr\'{e}s and Spieksma, Frits},
title = {{Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {11:1--11:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.11},
URN = {urn:nbn:de:0030-drops-249197},
doi = {10.4230/LIPIcs.ISAAC.2025.11},
annote = {Keywords: Diversity, Lattice Theory, Submodular Function Minimization}
}
Document
Star-Based Separators for Intersection Graphs of c-Colored Pseudo-Segments
Abstract
The Planar Separator Theorem, which states that any planar graph 𝒢 has a separator consisting of O(√n) nodes whose removal partitions 𝒢 into components of size at most 2n/3, is a widely used tool to obtain fast algorithms on planar graphs. Intersection graphs of disks, which generalize planar graphs, do not admit such separators. It has recently been shown that disk graphs do admit so-called clique-based separators that consist of O(√n) cliques. This result has been generalized to intersection graphs of various other types of disk-like objects. Unfortunately, segment intersection graphs do not admit small clique-based separators, because they can contain arbitrarily large bicliques. This is true even in the simple case of axis-aligned segments.
In this paper we therefore introduce biclique-based separators (and, in particular, star-based separators), which are separators consisting of a small number of bicliques (or stars). We prove that any c-oriented set of n segments in the plane, where c is a constant, admits a star-based separator consisting of O(√n) stars. In fact, our result is more general, as it applies to any set of n pseudo-segments that is partitioned into c subsets such that the pseudo-segments in the same subset are pairwise disjoint. We extend our result to intersection graphs of c-oriented polygons. These results immediately lead to an almost-exact distance oracle for such intersection graphs, which has O(n√n) storage and O(√n) query time, and that can report the hop-distance between any two query nodes in the intersection graph with an additive error of at most 2. This is the first distance oracle for such types of intersection graphs that has subquadratic storage and sublinear query time and that only has an additive error.
Cite as
Mark de Berg, Bart M. P. Jansen, and Jeroen S. K. Lamme. Star-Based Separators for Intersection Graphs of c-Colored Pseudo-Segments. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{deberg_et_al:LIPIcs.ISAAC.2025.12,
author = {de Berg, Mark and Jansen, Bart M. P. and Lamme, Jeroen S. K.},
title = {{Star-Based Separators for Intersection Graphs of c-Colored Pseudo-Segments}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {12:1--12:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.12},
URN = {urn:nbn:de:0030-drops-249207},
doi = {10.4230/LIPIcs.ISAAC.2025.12},
annote = {Keywords: Computational geometry, intersection graphs, biclique-based separators, distance oracles}
}
Document
Optimal Online Bipartite Matching in Degree-2 Graphs
Abstract
Online bipartite matching is a classical problem in online algorithms and we know that both the deterministic fractional and randomized integral online matchings achieve the same competitive ratio of 1-1/e. In this work, we study classes of graphs where the online degree is restricted to 2. As expected, one can achieve a competitive ratio of better than 1-1/e in both the deterministic fractional and randomized integral cases, but surprisingly, these ratios are not the same. It was already known that for fractional matching, a 0.75 competitive ratio algorithm is optimal. We show that the folklore Half-Half algorithm achieves a competitive ratio of η ≈ 0.717772… and more surprisingly, show that this is optimal by giving a matching lower-bound. This yields a separation between the two problems: deterministic fractional and randomized integral, showing that it is impossible to obtain a perfect rounding scheme.
Cite as
Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha. Optimal Online Bipartite Matching in Degree-2 Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bhangale_et_al:LIPIcs.ISAAC.2025.13,
author = {Bhangale, Amey and Chakraborty, Arghya and Harsha, Prahladh},
title = {{Optimal Online Bipartite Matching in Degree-2 Graphs}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {13:1--13:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.13},
URN = {urn:nbn:de:0030-drops-249216},
doi = {10.4230/LIPIcs.ISAAC.2025.13},
annote = {Keywords: Online Algorithm, Bipartite matching}
}
Document
On the (In)Approximability of the Monitoring Edge Geodetic Set Problem
Abstract
We study the minimum Monitoring Edge Geodetic Set (MEG-Set) problem introduced in [Foucaud et al., CALDAM'23]: given a graph G, we say that an edge is monitored by a pair u,v of vertices if all shortest paths between u and v traverse e; the goal is to find a subset M of vertices of G such that each edge of G is monitored by at least one pair of vertices in M, and |M| is minimized.
In this paper, we prove that all polynomial-time approximation algorithms for the minimum MEG-Set problem must have an approximation ratio of Ω(log n), unless 𝖯 = NP. To the best of our knowledge, this is the first non-constant inapproximability result known for this problem. We also strengthen the known NP-hardness of the problem on 2-apex graphs by showing that the same result holds for 1-apex graphs. This leaves open the question of determining whether the problem remains NP-hard on planar (i.e., 0-apex) graphs.
On the positive side, we design an algorithm that computes good approximate solutions for hereditary graph classes that admit efficiently computable balanced separators of truly sublinear size. This immediately yields polynomial-time approximation algorithms achieving an approximation ratio of O(n^{1/4} √{log n}) on planar graphs, graphs with bounded genus, and k-apex graphs with k = O(n^{1/4}). On graphs with bounded treewidth, we obtain an approximation ratio of O(log^{3/2} n). This compares favorably with the best-known approximation algorithm for general graphs, which achieves an approximation ratio of O(√{n log n}) via a simple reduction to the Set Cover problem.
Cite as
Davide Bilò, Giordano Colli, Luca Forlizzi, and Stefano Leucci. On the (In)Approximability of the Monitoring Edge Geodetic Set Problem. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bilo_et_al:LIPIcs.ISAAC.2025.14,
author = {Bil\`{o}, Davide and Colli, Giordano and Forlizzi, Luca and Leucci, Stefano},
title = {{On the (In)Approximability of the Monitoring Edge Geodetic Set Problem}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {14:1--14:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.14},
URN = {urn:nbn:de:0030-drops-249226},
doi = {10.4230/LIPIcs.ISAAC.2025.14},
annote = {Keywords: Monitoring Edge Geodetic Set, Inapproximability, Approximation Algorithms}
}
Document
Parameterized Complexity of Directed Traveling Salesman Problem
Abstract
The Directed Traveling Salesman Problem (DTSP) is a variant of the classical Traveling Salesman Problem in which the edges in the graph are directed and a vertex and edge can be visited multiple times. The goal is to find a directed closed walk of minimum length (or total weight) that visits every vertex of the given graph at least once. In a yet more general version, Directed Waypoint Routing Problem (DWRP), some vertices are marked as terminals and we are only required to visit all terminals. Furthermore, each edge has its capacity bounding the number of times this edge can be used by a solution.
While both problems (and many other variants of TSP) were extensively investigated, mostly from the approximation point of view, there are surprisingly few results concerning the parameterized complexity. Our starting point is the result of Marx et al. [APPROX/RANDOM 2016] who proved that DTSP is W[1]-hard parameterized by distance to pathwidth 3. In this paper we aim to initiate the systematic complexity study of variants of Directed Traveling Salesman Problem with respect to various, mostly structural, parameters.
We show that DWRP is FPT parameterized by the solution size, the feedback edge number and the vertex integrity of the underlying undirected graph. Furthermore, the problem is XP parameterized by treewidth.
On the complexity side, we show that the problem is W[1]-hard parameterized by the distance to constant treedepth.
Cite as
Václav Blažej, Andreas Emil Feldmann, Foivos Fioravantes, Paweł Rzążewski, and Ondřej Suchý. Parameterized Complexity of Directed Traveling Salesman Problem. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{blazej_et_al:LIPIcs.ISAAC.2025.15,
author = {Bla\v{z}ej, V\'{a}clav and Feldmann, Andreas Emil and Fioravantes, Foivos and Rz\k{a}\.{z}ewski, Pawe{\l} and Such\'{y}, Ond\v{r}ej},
title = {{Parameterized Complexity of Directed Traveling Salesman Problem}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {15:1--15:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.15},
URN = {urn:nbn:de:0030-drops-249231},
doi = {10.4230/LIPIcs.ISAAC.2025.15},
annote = {Keywords: Directed TSP, parameterized complexity, vertex integrity, treedepth}
}
Document
A Dichotomy for 1-Planarity with Restricted Crossing Types Parameterized by Treewidth
Abstract
A drawing of a graph is 1-planar if each edge participates in at most one crossing and adjacent edges do not cross. Up to symmetry, each crossing in a 1-planar drawing belongs to one out of six possible crossing types, where a type characterizes the subgraph induced by the four vertices of the crossing edges. Each of the 63 possible nonempty subsets 𝒮 of crossing types gives a recognition problem: does a given graph admit an 𝒮-restricted drawing, that is, a 1-planar drawing where the crossing type of each crossing is in 𝒮?
We show that there is a set 𝒮_bad with three crossing types and the following properties:
- If 𝒮 contains no crossing type from 𝒮_bad, then the recognition of graphs that admit an 𝒮-restricted drawing is fixed-parameter tractable with respect to the treewidth of the input graph.
- If 𝒮 contains any crossing type from 𝒮_bad, then it is NP-hard to decide whether a graph has an 𝒮-restricted drawing, even when considering graphs of constant pathwidth. We also extend this characterization of crossing types to 1-planar straight-line drawings and show the same complexity behaviour parameterized by treewidth.
Cite as
Sergio Cabello, Alexander Dobler, Gašper Fijavž, Thekla Hamm, and Mirko H. Wagner. A Dichotomy for 1-Planarity with Restricted Crossing Types Parameterized by Treewidth. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{cabello_et_al:LIPIcs.ISAAC.2025.16,
author = {Cabello, Sergio and Dobler, Alexander and Fijav\v{z}, Ga\v{s}per and Hamm, Thekla and Wagner, Mirko H.},
title = {{A Dichotomy for 1-Planarity with Restricted Crossing Types Parameterized by Treewidth}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {16:1--16:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.16},
URN = {urn:nbn:de:0030-drops-249248},
doi = {10.4230/LIPIcs.ISAAC.2025.16},
annote = {Keywords: 1-planar, crossing type, treewidth, pathwidth}
}
Document
Realization of Temporally Connected Graphs Based on Degree Sequences
Abstract
Given an undirected graph G, the problem of deciding whether G admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (Göbel et al., 1991). In this article, we relax this problem and ask whether a given degree sequence can be realized as a temporally connected graph. Our main results are a complete characterization of the feasible cases, and a recognition algorithm that runs in 𝒪(n) time for graphical degree sequences (realized as simple temporal graphs) and in 𝒪(n+m) time for multigraphical degree sequences (realized as non-simple temporal graphs, where the number of time labels on an edge corresponds to the multiplicity of the edge in the multigraph). In fact, these algorithms can be made constructive at essentially no cost. Namely, we give a constructive 𝒪(n+m) time algorithm that outputs, for a given (multi)graphical degree sequence 𝐝, a temporally connected graph whose underlying (multi)graph is a realization of 𝐝, if one exists.
Cite as
Arnaud Casteigts, Michelle Döring, and Nils Morawietz. Realization of Temporally Connected Graphs Based on Degree Sequences. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{casteigts_et_al:LIPIcs.ISAAC.2025.17,
author = {Casteigts, Arnaud and D\"{o}ring, Michelle and Morawietz, Nils},
title = {{Realization of Temporally Connected Graphs Based on Degree Sequences}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {17:1--17:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.17},
URN = {urn:nbn:de:0030-drops-249256},
doi = {10.4230/LIPIcs.ISAAC.2025.17},
annote = {Keywords: temporal paths, gossiping, (multi)graphical degree sequences, edge-disjoint spanning trees, linear time algorithms}
}
Document
An Optimal Algorithm for the Stacker Crane Problem on Fixed Topologies
Abstract
The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its respective delivery point. The goal is to minimize the total distance traveled. SCP is known to be NP-hard, even on trees. The only positive results, in terms of polynomial-time solvability, apply to graphs that are topologically equivalent to a path or a cycle.
We propose an algorithm that is optimal for each fixed topology, running in near-linear time. This is achieved by demonstrating that the problem is fixed-parameter tractable (FPT) when parameterized by both the cycle rank and the number of branch vertices.
Cite as
Yike Chen, Ke Shi, and Chao Xu. An Optimal Algorithm for the Stacker Crane Problem on Fixed Topologies. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 18:1-18:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{chen_et_al:LIPIcs.ISAAC.2025.18,
author = {Chen, Yike and Shi, Ke and Xu, Chao},
title = {{An Optimal Algorithm for the Stacker Crane Problem on Fixed Topologies}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {18:1--18:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.18},
URN = {urn:nbn:de:0030-drops-249269},
doi = {10.4230/LIPIcs.ISAAC.2025.18},
annote = {Keywords: Stacker Crane Problem, Fixed-Parameter Tractable, Min-Cost Circulation}
}
Document
Traffic-Oblivious Multi-Commodity Flow Network Design
Abstract
We consider the Minimum Multi-Commodity Flow Subgraph (MMCFS) problem: given a directed graph G with edge capacities cap and a retention ratio α ∈ (0,1), find an edge-wise minimum subgraph G' ⊆ G such that for all traffic matrices T routable in G using a multi-commodity flow, α⋅ T is routable in G'. This natural yet novel problem is motivated by recent research that investigates how the power consumption in backbone computer networks can be reduced by turning off connections during times of low demand without compromising the quality of service. Since the actual traffic demands are generally not known beforehand, our approach must be traffic-oblivious, i.e., work for all possible sets of simultaneously routable traffic demands in the original network.
In this paper we present the problem, relate it to other known problems in literature, and show several structural results, including a reformulation, maximum possible deviations from the optimum, and NP-hardness (as well as a certain inapproximability) already on very restricted instances. The most significant contribution is a max(1/α, 2)-approximation based on a surprisingly simple LP-rounding scheme. We also give instances where this worst-case approximation ratio is met and thus prove that our analysis is tight.
Cite as
Markus Chimani and Max Ilsen. Traffic-Oblivious Multi-Commodity Flow Network Design. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{chimani_et_al:LIPIcs.ISAAC.2025.19,
author = {Chimani, Markus and Ilsen, Max},
title = {{Traffic-Oblivious Multi-Commodity Flow Network Design}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {19:1--19:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.19},
URN = {urn:nbn:de:0030-drops-249273},
doi = {10.4230/LIPIcs.ISAAC.2025.19},
annote = {Keywords: Multi-commodity flow, Digraphs, LP-rounding, Approximation algorithm}
}
Document
Sparse Induced Subgraphs in P₇-Free Graphs of Bounded Clique Number
Abstract
Many natural computational problems, including e.g. Max Weight Independent Set, Feedback Vertex Set, or Vertex Planarization, can be unified under an umbrella of finding the largest sparse induced subgraph that satisfies some property definable in CMSO₂ logic. It is believed that each problem expressible with this formalism can be solved in polynomial time in graphs that exclude a fixed path as an induced subgraph. This belief is supported by the existence of a quasipolynomial-time algorithm by Gartland, Lokshtanov, Pilipczuk, Pilipczuk, and Rzążewski [STOC 2021], and a recent polynomial-time algorithm for P₆-free graphs by Chudnovsky, McCarty, Pilipczuk, Pilipczuk, and Rzążewski [SODA 2024].
In this work we extend polynomial-time tractability of all such problems to P₇-free graphs of bounded clique number.
Cite as
Maria Chudnovsky, Jadwiga Czyżewska, Kacper Kluk, Marcin Pilipczuk, and Paweł Rzążewski. Sparse Induced Subgraphs in P₇-Free Graphs of Bounded Clique Number. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 20:1-20:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{chudnovsky_et_al:LIPIcs.ISAAC.2025.20,
author = {Chudnovsky, Maria and Czy\.{z}ewska, Jadwiga and Kluk, Kacper and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l}},
title = {{Sparse Induced Subgraphs in P₇-Free Graphs of Bounded Clique Number}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {20:1--20:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.20},
URN = {urn:nbn:de:0030-drops-249282},
doi = {10.4230/LIPIcs.ISAAC.2025.20},
annote = {Keywords: P\underlinet-free graphs, maximum weight induced subgraph, maximum weight independent set}
}
Document
Covering Weighted Points Using Unit Squares
Abstract
Given a set of n points in d-dimensional space, each assigned a positive weight, we study the problem of finding k axis-parallel unit hypercubes that maximize the total weight of the points contained in their union. In this paper, we present both exact and (1 - ε)-approximation algorithms for the case of k = 2. We present an exact algorithm that runs in O(n²) time in the plane, improving the previous O(n² log² n)-time result. This algorithm generalizes to higher dimensions and larger k in O(n^{dk/2}) time for fixed d and k. We also present a (1 - ε)-approximation algorithm that runs in O(n log min{n, 1/ε} + 1/ε³) time for k = 2 in the plane, improving the best known result. Our approximation algorithm also extends to higher dimensions.
Cite as
Chaeyoon Chung, Jaegun Lee, and Hee-Kap Ahn. Covering Weighted Points Using Unit Squares. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{chung_et_al:LIPIcs.ISAAC.2025.21,
author = {Chung, Chaeyoon and Lee, Jaegun and Ahn, Hee-Kap},
title = {{Covering Weighted Points Using Unit Squares}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {21:1--21:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.21},
URN = {urn:nbn:de:0030-drops-249292},
doi = {10.4230/LIPIcs.ISAAC.2025.21},
annote = {Keywords: Maximum coverage, Unit squares, Approximation algorithms}
}
Document
Minimum Partition of Polygons Under Width and Cut Constraints
Abstract
We study the problem of partitioning a polygon into the minimum number of subpolygons using cuts in predetermined directions such that each resulting subpolygon satisfies a given width constraint. A polygon satisfies the unit-width constraint for a set of unit vectors if the length of the orthogonal projection of the polygon on a line parallel to a vector in the set is at most one. We analyze structural properties of the minimum partition numbers, focusing on monotonicity under polygon containment. We show that the minimum partition number of a simple polygon is at least that of any subpolygon, provided that the subpolygon satisfies a certain orientation-wise convexity with respect to the polygon. As a consequence, we prove a partition analogue of the Bang’s conjecture about coverings of convex regions in the plane: for any partition of a convex body in the plane, the sum of relative widths of all parts is at least one. For any convex polygon, there exists a direction along which an optimal partition is achieved by parallel cuts. Given such a direction, an optimal partition can be computed in linear time.
Cite as
Jaehoon Chung, Kazuo Iwama, Chung-Shou Liao, and Hee-Kap Ahn. Minimum Partition of Polygons Under Width and Cut Constraints. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{chung_et_al:LIPIcs.ISAAC.2025.22,
author = {Chung, Jaehoon and Iwama, Kazuo and Liao, Chung-Shou and Ahn, Hee-Kap},
title = {{Minimum Partition of Polygons Under Width and Cut Constraints}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {22:1--22:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.22},
URN = {urn:nbn:de:0030-drops-249302},
doi = {10.4230/LIPIcs.ISAAC.2025.22},
annote = {Keywords: Polygon partitioning, Width constraints, Plank problem}
}
Document
Precoloring Extension with Demands on Paths
Abstract
Let G be a graph with a set of precolored vertices, and let us be given an integer distance parameter d and a set of integer demands d₁,… ,d_c. The Distance Precoloring Extension with Demands (DPED) problem is to compute a vertex c-coloring of G such that the following three conditions hold: (i) the resulting coloring respects the colors of the precolored vertices, (ii) the distance of two vertices of the same color is at least d, and (iii) the number of vertices colored by color i is exactly d_i. This problem is motivated by a program scheduling in commercial broadcast channels with constraints on content repetition and placement, which leads precisely to the DPED problem for paths.
In this paper, we study DPED on paths and present a polynomial time exact algorithm when precolored vertices are restricted to the two ends of the path and devise an approximation algorithm for DPED with an additive approximation factor polynomially bounded by d and the number of precolored vertices. Then, we prove that the Distance Precoloring Extension problem on paths, a less restrictive version of DPED without the demand constraints, and then DPED itself, is NP-complete. Motivated by this result, we further study the parameterized complexity of DPED on paths. We establish that the DPED problem on paths is W[1]-hard when parameterized by the number of colors and the distance. On the positive side, we devise a fixed parameter tractable (FPT) algorithm for DPED on paths when the number of colors, the distance, and the number of precolored vertices are considered as the parameters. Moreover, we prove that Distance Precoloring Extension is FPT parameterized by the distance. As a byproduct, we also obtain several results for the Distance List Coloring problem on paths.
Cite as
Arun Kumar Das, Michal Opler, and Tomáš Valla. Precoloring Extension with Demands on Paths. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{das_et_al:LIPIcs.ISAAC.2025.23,
author = {Das, Arun Kumar and Opler, Michal and Valla, Tom\'{a}\v{s}},
title = {{Precoloring Extension with Demands on Paths}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {23:1--23:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.23},
URN = {urn:nbn:de:0030-drops-249319},
doi = {10.4230/LIPIcs.ISAAC.2025.23},
annote = {Keywords: precoloring extension, distance coloring, FPT, approximation algorithms}
}
Document
Enumerating the Irreducible Closed Sets of an Acyclic Implicational Base of Bounded Degree
Abstract
We consider the problem of enumerating the irreducible closed sets of a closure system given by an implicational base. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph dualization problem, even in the case of acyclic convex geometries, i.e., closure systems admitting an acyclic implicational base. This paper studies this case with a focus on the degree, which corresponds to the maximal number of implications in which an element occurs. We show that the problem is tractable for bounded values of this parameter, even when relaxed to the notions of premise- and conclusion-degree. Our algorithms rely on a sequential approach leveraging from acyclicity, combined with the solution graph traversal technique for the case of premise-degree. They are shown to perform in incremental-polynomial time. These results are complemented in the long version of this document by showing that the dual problem of constructing the implicational base can be solved in polynomial time. Finally, we argue that our running times cannot be improved to polynomial delay using the standard framework of flashlight search.
Cite as
Oscar Defrain, Arthur Ohana, and Simon Vilmin. Enumerating the Irreducible Closed Sets of an Acyclic Implicational Base of Bounded Degree. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{defrain_et_al:LIPIcs.ISAAC.2025.24,
author = {Defrain, Oscar and Ohana, Arthur and Vilmin, Simon},
title = {{Enumerating the Irreducible Closed Sets of an Acyclic Implicational Base of Bounded Degree}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {24:1--24:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.24},
URN = {urn:nbn:de:0030-drops-249321},
doi = {10.4230/LIPIcs.ISAAC.2025.24},
annote = {Keywords: Algorithmic enumeration, closure systems, acyclic convex geometries, solution graph traversal, flashlight search, extension, hypergraph dualization}
}
Document
Structural Parameterizations of Simultaneous Planarity
Abstract
Given a set of graphs on the same vertex set, the problem Simultaneous Embedding With Fixed Edges (SEFE) asks, whether there exist planar drawings of all input graphs, such that every pair of drawings coincides on their shared subgraph. It is known that SEFE is NP-complete [Elisabeth Gassner et al., 2006], even in the so-called sunflower case, where all pairs of input graphs have the same shared graph G_∩ [Marcus Schaefer, 2012]. Fink, Pfretzschner, and Rutter [Simon D. Fink et al., 2023] recently initiated the study of the parameterized complexity of SEFE in the sunflower case, mainly focusing on structural parameters of G_∩. In this work, we shift the focus towards parameters of the union graph G_∪ that contains the edges of all input graphs. On the positive side, we establish fixed-parameter tractability for the problem with respect to the feedback edge set number of G_∪. We complement this result by showing that it, surprisingly, remains NP-complete even if G_∪ has constant vertex cover number. These results settle two open questions posed by Fink et al. [Simon D. Fink et al., 2023].
Cite as
Thomas Depian, Simon D. Fink, Alexander Firbas, Robert Ganian, Matthias Pfretzschner, and Ignaz Rutter. Structural Parameterizations of Simultaneous Planarity. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{depian_et_al:LIPIcs.ISAAC.2025.25,
author = {Depian, Thomas and Fink, Simon D. and Firbas, Alexander and Ganian, Robert and Pfretzschner, Matthias and Rutter, Ignaz},
title = {{Structural Parameterizations of Simultaneous Planarity}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {25:1--25:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.25},
URN = {urn:nbn:de:0030-drops-249332},
doi = {10.4230/LIPIcs.ISAAC.2025.25},
annote = {Keywords: SEFE, Simultaneous Planarity, Fixed-Parameter Tractability, NP-hardness}
}
Document
A Tight Lower Bound for Online Service with Deadlines and Lazy Server
Abstract
We study the online service with deadlines (or delays) problem, in which a server must serve requests for points in a metric space while balancing travel distance and promptness of service. While the problem has been extensively studied (STOC 2017), (FOCS 2019), (FOCS 2023), the main open question whether a constant competitive ratio can be achieved remains wide open. We prove a logarithmic lower bound for a natural class of algorithms already on uniform line metrics. Our lower bound applies to, and is tight for, the best known algorithms for general metrics and uniform line metrics.
Cite as
Yann Disser and Linda Thelen. A Tight Lower Bound for Online Service with Deadlines and Lazy Server. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{disser_et_al:LIPIcs.ISAAC.2025.26,
author = {Disser, Yann and Thelen, Linda},
title = {{A Tight Lower Bound for Online Service with Deadlines and Lazy Server}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {26:1--26:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.26},
URN = {urn:nbn:de:0030-drops-249347},
doi = {10.4230/LIPIcs.ISAAC.2025.26},
annote = {Keywords: online algorithms, competitive analysis, lower bound, delay, deadlines}
}
Document
Simple, Strict, Proper, and Directed: Comparing Reachability in Directed and Undirected Temporal Graphs
Abstract
Temporal graphs model networks whose connections are available only at specific points in time. Several definitional subtleties - whether paths must follow strictly increasing time labels (strict vs. non-strict), whether adjacent edges cannot appear simultaneously (proper), and whether edges are forbidden to appear multiple times (simple) - give rise to different temporal graph settings. These distinctions directly impact the definition of temporal reachability, a core concept in temporal graph theory. Casteigts, Corsini, and Sarkar [TCS24] introduced a framework of equivalence notions to compare the expressive power of these settings focusing solely on undirected temporal graphs. In this work, we extend their framework to include the fundamental dimension of directed vs. undirected.
Our contribution is three-fold. We (1) complete the undirected hierarchy by resolving the two open questions from [TCS24], (2) fully characterize the hierarchy of the directed settings, and (3) compare the directed and undirected settings, showing that directed temporal graphs are strictly more expressive than undirected temporal graphs in terms of reachability.
Our structural results highlight both the limitations and strengths of various temporal graph settings - for example, directed + strict + simple graphs can realize every possible reachability graph, while directed + proper graphs necessarily induce at least one transitive reachability on each directed cycle. We also provide transformation procedures between temporal settings offering practical tools for transferring algorithms and hardness results across models.
Cite as
Michelle Döring. Simple, Strict, Proper, and Directed: Comparing Reachability in Directed and Undirected Temporal Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{doring:LIPIcs.ISAAC.2025.27,
author = {D\"{o}ring, Michelle},
title = {{Simple, Strict, Proper, and Directed: Comparing Reachability in Directed and Undirected Temporal Graphs}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {27:1--27:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.27},
URN = {urn:nbn:de:0030-drops-249353},
doi = {10.4230/LIPIcs.ISAAC.2025.27},
annote = {Keywords: temporal graphs, directed graphs, temporal reachability, dynamic networks}
}
Document
Pathfinding in Self-Deleting Graphs
Abstract
In this paper, we study the problem of pathfinding on traversal-dependent graphs, i.e., graphs whose edges change depending on the previously visited vertices. In particular, we study self-deleting graphs, introduced by Carmesin et al. [Sarah Carmesin et al., 2023], which consist of a graph G = (V, E) and a function f: V → 2^E, where f(v) is the set of edges that will be deleted after visiting the vertex v. In the (Shortest) Self-Deleting s-t-path problem we are given a self-deleting graph and its vertices s and t, and we are asked to find a (shortest) path from s to t, such that it does not traverse an edge in f(v) after visiting v for any vertex v.
We prove that Self-Deleting s-t-path is NP-hard even if the given graph is outerplanar, bipartite, has maximum degree 3, bandwidth 2 and |f(v)| ≤ 1 for each vertex v. We show that Shortest Self-Deleting s-t-path is W[1]-complete parameterized by the length of the sought path and that Self-Deleting s-t-path is W[1]-complete parameterized by the vertex cover number, feedback vertex set number and treedepth. We also show that the problem becomes FPT when we parameterize by the maximum size of f(v) and several structural parameters. Lastly, we show that the problem does not admit a polynomial kernel even for parameterization by the vertex cover number and the maximum size of f(v) combined already on 2-outerplanar graphs.
Cite as
Michal Dvořák, Dušan Knop, Michal Opler, Jan Pokorný, Ondřej Suchý, and Krisztina Szilágyi. Pathfinding in Self-Deleting Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{dvorak_et_al:LIPIcs.ISAAC.2025.28,
author = {Dvo\v{r}\'{a}k, Michal and Knop, Du\v{s}an and Opler, Michal and Pokorn\'{y}, Jan and Such\'{y}, Ond\v{r}ej and Szil\'{a}gyi, Krisztina},
title = {{Pathfinding in Self-Deleting Graphs}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {28:1--28:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.28},
URN = {urn:nbn:de:0030-drops-249365},
doi = {10.4230/LIPIcs.ISAAC.2025.28},
annote = {Keywords: Parameterized complexity, self-deleting graphs, pathfinding}
}
Document
Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings
Abstract
We call a graph G separable if a balanced separator can be computed for G of size O(n^ε) with ε < 1. Many real-world graphs are separable such as graphs of bounded genus, graphs of constant treewidth, and graphs excluding a fixed minor. In particular, the well-known planar graphs are separable. We present a succinct encoding of separable graphs G such that, after the encoding is computed, any number of depth-first searches (DFS) can be performed from any given start vertex, each in o(n) time and o(n) bits in the word RAM model. After the execution of a DFS, the succinct encoding of G is augmented such that the DFS tree is encoded inside the encoding while maintaining succinctness. Afterward, the encoding provides common DFS-related queries in constant time. These queries include queries such as lowest-common ancestor of two given vertices in the DFS tree or queries that output the lowpoint of a given vertex in the DFS tree. Furthermore, for planar graphs, we show that the succinct encoding can be computed in O(n) bits and expected linear time, and a compact variant can be constructed in O(n) time and bits. For other separable graph classes 𝒢 the runtime and space usage depends on the specific algorithms used to find balanced separators in graphs of 𝒢.
Cite as
Michael Elberfeld, Frank Kammer, and Johannes Meintrup. Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{elberfeld_et_al:LIPIcs.ISAAC.2025.29,
author = {Elberfeld, Michael and Kammer, Frank and Meintrup, Johannes},
title = {{Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {29:1--29:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.29},
URN = {urn:nbn:de:0030-drops-249379},
doi = {10.4230/LIPIcs.ISAAC.2025.29},
annote = {Keywords: Depth-First Search, Succinct, Space Efficient, Separable Graphs, Planar Graphs, Table Lookup, r-Division}
}
Document
Incidences Between Curves and Points on the Grid
Abstract
We derive an improved upper bound for the number of incidences between the n vertices of a uniform grid and m convex or concave curves, each pair of which intersect in at most s points, for some integer parameter s ≥ 1. For a square grid, our bound is O(n^{2/3}m^{2/3} + m^{1-1/(3s)} n^{(s+1)/3s} + m + n) . This improves a general bound of O(m n^{1/3}) on the number of incidences with respect to vertices of a grid and convex or concave curves.
For a rectangular grid, which fits inside a 1×K rectangle, for some integer K > 1 (which generally may depend on n), the bound also depends on how large K is. The precise result is stated in Theorem 2, but, roughly, we get the same bound as above when K is not too large.
Our analysis competes with a celebrated result of Bombieri and Pila [E. Bombieri and J. Pila, 1989], which gives (usually) a sharper bound if we assume that the input curves are algebraic of constant degree and the input points are vertices of the square grid. However, the analysis in [E. Bombieri and J. Pila, 1989] strongly relies on these assumptions, and cannot be extended to handle the more general setup considered here.
As a main application, of independent interest, we present a variant of our technique for semi-algebraic range reporting on sets of points of "bounded spread" in the plane.
Cite as
Esther Ezra and Micha Sharir. Incidences Between Curves and Points on the Grid. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{ezra_et_al:LIPIcs.ISAAC.2025.30,
author = {Ezra, Esther and Sharir, Micha},
title = {{Incidences Between Curves and Points on the Grid}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {30:1--30:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.30},
URN = {urn:nbn:de:0030-drops-249387},
doi = {10.4230/LIPIcs.ISAAC.2025.30},
annote = {Keywords: Geometric incidences, uniform grid, bounded spread, Pick’s theorem, range searching}
}
Document
Compressibility Measures and Succinct Data Structures for Piecewise Linear Approximations
Abstract
We study the problem of deriving compressibility measures for Piecewise Linear Approximations (PLAs), i.e., error-bounded approximations of a set of two-dimensional increasing data points using a sequence of segments. Such approximations are widely used tools in implementing many learned data structures, which mix learning models with traditional algorithmic design blocks to exploit regularities in the underlying data distribution, providing novel and effective space-time trade-offs.
We introduce the first lower bounds to the cost of storing PLAs in two settings, namely compression and indexing. We then compare these compressibility measures to known data structures, and show that they are asymptotically optimal up to a constant factor from the space lower bounds. Finally, we design the first data structures for the aforementioned settings that achieve the space lower bounds plus small additive terms, which turn out to be succinct in most practical cases. Our data structures support the efficient retrieval and evaluation of a segment in the (compressed) PLA for a given x-value, which is a core operation in any learned data structure relying on PLAs.
As a result, our paper offers the first theoretical analysis of the maximum compressibility achievable by PLA-based learned data structures, and provides novel storage schemes for PLAs offering strong theoretical guarantees while also suggesting simple and efficient practical implementations.
Cite as
Paolo Ferragina and Filippo Lari. Compressibility Measures and Succinct Data Structures for Piecewise Linear Approximations. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 31:1-31:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{ferragina_et_al:LIPIcs.ISAAC.2025.31,
author = {Ferragina, Paolo and Lari, Filippo},
title = {{Compressibility Measures and Succinct Data Structures for Piecewise Linear Approximations}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {31:1--31:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.31},
URN = {urn:nbn:de:0030-drops-249397},
doi = {10.4230/LIPIcs.ISAAC.2025.31},
annote = {Keywords: Piecewise Linear Approximations, Succinct Data Structures, Lower Bounds}
}
Document
Time-Optimal k-Server
Abstract
The time-optimal k-server problem minimizes the time spent instead of the distance traveled when serving n requests, appearing one after the other, with k servers in a metric space. The classical distance model was motivated by a hard disk with k heads. Instead of minimal head movements, the time model aims for optimal reading speeds.
This paper provides a lower bound of 2k-1 on the competitive ratio of any deterministic online algorithm for the time-optimal k-server problem on a specifically designed metric space. This lower bound coincides with the best known upper bound on the competitive ratio for the classical k-server problem, achieved by the famous work function algorithm. We provide further lower bounds of k+1 for all Euclidean spaces and k for uniform metric spaces.
Our most technical result, proven by applying Yao’s principle to a suitable instance distribution, is a lower bound of k+H_k-1 that holds even for randomized algorithms, which contrasts with the best known lower bound for the classical problem, which is polylogarithmic in k.
We hope to initiate further intensive study of this natural problem.
Cite as
Fabian Frei, Dennis Komm, Moritz Stocker, and Philip Whittington. Time-Optimal k-Server. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{frei_et_al:LIPIcs.ISAAC.2025.32,
author = {Frei, Fabian and Komm, Dennis and Stocker, Moritz and Whittington, Philip},
title = {{Time-Optimal k-Server}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {32:1--32:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.32},
URN = {urn:nbn:de:0030-drops-249407},
doi = {10.4230/LIPIcs.ISAAC.2025.32},
annote = {Keywords: k-server problem, optimizing time instead of distance, deterministic and randomized algorithms, Yao’s principle}
}
Document
Coloring Reconfiguration Under Color Swapping
Abstract
In the Coloring Reconfiguration problem, we are given two proper k-colorings of a graph and asked to decide whether one can be transformed into the other by repeatedly applying a specified recoloring rule, while maintaining a proper coloring throughout. For this problem, two recoloring rules have been widely studied: single-vertex recoloring and Kempe chain recoloring. In this paper, we introduce a new rule, called color swapping, where two adjacent vertices may exchange their colors, so that the resulting coloring remains proper, and study the computational complexity of the problem under this rule. We first establish a complexity dichotomy with respect to k: the problem is solvable in polynomial time for k ≤ 2, and is PSPACE-complete for k ≥ 3. We further show that the problem remains PSPACE-complete even on restricted graph classes, including bipartite graphs, split graphs, and planar graphs of bounded degree. In contrast, we present polynomial-time algorithms for several graph classes: for paths when k = 3, for split graphs when k is fixed, and for cographs when k is arbitrary.
Cite as
Janosch Fuchs, Rin Saito, Tatsuhiro Suga, Takahiro Suzuki, and Yuma Tamura. Coloring Reconfiguration Under Color Swapping. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{fuchs_et_al:LIPIcs.ISAAC.2025.33,
author = {Fuchs, Janosch and Saito, Rin and Suga, Tatsuhiro and Suzuki, Takahiro and Tamura, Yuma},
title = {{Coloring Reconfiguration Under Color Swapping}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {33:1--33:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.33},
URN = {urn:nbn:de:0030-drops-249411},
doi = {10.4230/LIPIcs.ISAAC.2025.33},
annote = {Keywords: Combinatorial reconfiguration, graph coloring, PSPACE-complete, graph algorithm}
}
Document
Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice
Abstract
Radio Networks (RN) is one of the fundamental models for network communication where nodes can broadcast messages locally but their simultaneous transmissions can interfere with each other at their shared neighbors. This work focuses on performing the very fundamental primitive of Local Broadcast, in spite of the interferences.
We investigate to what extent local knowledge, called advice, relating to the 2-local domination number γ₂ may speed up Local Broadcast. Specifically for each node and some dominating set, knowledge about some neighboring dominating node and the local number among the neighbors of that dominating node. We show that such advice is sufficient to build an efficient oblivious transmission schedule. Along those lines, we present three algorithms trading the level of adaptiveness (from oblivious to adaptive) for bits of advice per node (from O(log (Δγ₂)) to 1). All our algorithms complete Local Broadcast in Õ(Δγ₂²) rounds, where Δ is the maximum degree of the network.
On the side of lower bounds, we show that, for each quasi-adaptive deterministic Local Broadcast algorithm, there is some RN that requires Ω(min{(min{Δ,γ₂}/log n)²,n}) communication rounds, where n is the number of network nodes. In quasi-adaptive protocols nodes may stop executing once its computational task is completed. To the best of our knowledge, this is the first (nearly) quadratic Local Broadcast (same message for all neighbors) lower bound in the RN model. Our lower bound is stronger than previous works in multiple ways: i) it is nearly quadratically better than the best known general lower bound for this class of algorithms, ii) it applies to a wider class of algorithms than previous work for fully oblivious, iii) it achieves similar time lower bound than previous work proved for a much more demanding Local Broadcast where each node sends a possibly different message to each neighbor, and iv) it takes into account the local domination parameter γ₂.
Cite as
Pawel Garncarek, Tomasz Jurdzinski, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro. Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{garncarek_et_al:LIPIcs.ISAAC.2025.34,
author = {Garncarek, Pawel and Jurdzinski, Tomasz and Kowalski, Dariusz R. and Kutten, Shay and Mosteiro, Miguel A.},
title = {{Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {34:1--34:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.34},
URN = {urn:nbn:de:0030-drops-249426},
doi = {10.4230/LIPIcs.ISAAC.2025.34},
annote = {Keywords: Radio Networks, Local Broadcast, Distributed Deterministic Algorithms, Lower Bounds, Graph algorithms, Advice, Labeling Schemes, Local Domination}
}
Document
Anonymous Self-Stabilising Localisation via Spatial Population Protocols
Abstract
In the distributed localisation problem (DLP), n anonymous robots (agents) A_0, ..., A_{n-1} are located at arbitrary points p_0, ..., p_{n-1} ∈ S, where S is a Euclidean space. Initially, each agent A_i operates within its own coordinate system in S, which may be inconsistent with those of other agents. The primary goal in DLP is for agents to reach a consensus on a unified (jointly agreed) coordinate system, in which all agents receive unique labels (coordinates) that accurately reflect the relative distances between all points p_0, ..., p_{n-1} in S. Extensive research on DLP has primarily focus on the feasibility and complexity of achieving consensus when agents have limited access to inter-agent distances, often due to missing or imprecise data. In contrast, this paper proposes a minimalist, computationally efficient distributed computing model where agents can query any pairwise relative positions, if needed. Specifically, we introduce a novel variant of population protocols, referred to as the spatial population protocols model. In this variant each agent can memorise one or a fixed number of coordinates, and when agents A_i and A_j interact, they can not only exchange their current knowledge but also either determine the distance d_{ij} between them in S (distance query model) or obtain the vector v_{ij} spanning points p_i and p_j (vector query model).
We propose and analyse several distributed localisation protocols, including:
1) Leader-based localisation protocol with distance queries We propose and analyse two leader-based localisation protocols that stabilise silently in o(n) time. These protocols leverage an efficient solution to the novel concept of multi-contact epidemic, a natural generalisation of the core communication tool in population protocols, known as the one-way epidemic.
2) Self-stabilising leader localisation protocol with distance queries We show how to effectively utilise a leader election mechanism within the leader-based localisation protocol to get a DLP protocol that self-stabilises silently in time O(n(log n/n)^{1/(k+1)}log n) in k-dimensions.
3) Self-stabilising localisation protocol with vector queries We propose and analyse an optimally fast DLP protocol which self-stabilises silently in O(log n) time.
Cite as
Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak. Anonymous Self-Stabilising Localisation via Spatial Population Protocols. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{gasieniec_et_al:LIPIcs.ISAAC.2025.35,
author = {G\k{a}sieniec, Leszek and Kuszner, {\L}ukasz and Latif, Ehsan and Parasuraman, Ramviyas and Spirakis, Paul and Stachowiak, Grzegorz},
title = {{Anonymous Self-Stabilising Localisation via Spatial Population Protocols}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {35:1--35:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.35},
URN = {urn:nbn:de:0030-drops-249433},
doi = {10.4230/LIPIcs.ISAAC.2025.35},
annote = {Keywords: Population Protocols, Distributed Localisation, Spacial Queries, Self-Stabilisation}
}
Document
Streaming Periodicity with Mismatches, Wildcards, and Edits
Abstract
In this work, we study the problem of detecting periodic trends in strings. While detecting exact periodicity has been studied extensively, real-world data is often noisy, where small deviations or mismatches occur between repetitions. This work focuses on a generalized approach to period detection that efficiently handles noise. Given a string S of length n, the task is to identify integers p such that the prefix and the suffix of S, each of length n-p+1, are similar under a given distance measure. Ergün et al. [APPROX-RANDOM 2017] were the first to study this problem in the streaming model under the Hamming distance. In this work, we combine, in a non-trivial way, the Hamming distance sketch of Clifford et al. [SODA 2019] and the structural description of the k-mismatch occurrences of a pattern in a text by Charalampopoulos et al. [FOCS 2020] to present a more efficient streaming algorithm for period detection under the Hamming distance. As a corollary, we derive a streaming algorithm for detecting periods of strings which may contain wildcards, a special symbol that match any character of the alphabet. Our algorithm is not only more efficient than that of Ergün et al. [TCS 2020], but it also operates without their assumption that the string must be free of wildcards in its final characters. Additionally, we introduce the first two-pass streaming algorithm for computing periods under the edit distance by leveraging and extending the Bhattacharya-Koucký’s grammar decomposition technique [STOC 2023].
Cite as
Taha El Ghazi and Tatiana Starikovskaya. Streaming Periodicity with Mismatches, Wildcards, and Edits. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{elghazi_et_al:LIPIcs.ISAAC.2025.36,
author = {El Ghazi, Taha and Starikovskaya, Tatiana},
title = {{Streaming Periodicity with Mismatches, Wildcards, and Edits}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {36:1--36:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.36},
URN = {urn:nbn:de:0030-drops-249446},
doi = {10.4230/LIPIcs.ISAAC.2025.36},
annote = {Keywords: approximate periods, pattern matching, streaming algorithms}
}
Document
Parallel Joinable B-Trees in the Fork-Join I/O Model
Abstract
Balanced search trees are widely used in computer science to efficiently maintain dynamic ordered data. To support efficient set operations (e.g., union, intersection, difference) using trees, the join-based framework is widely studied. This framework has received particular attention in the parallel setting, and has been shown to be effective in enabling simple and theoretically efficient set operations on trees. Despite the widespread adoption of parallel join-based trees, a major drawback of previous work on such data structures is the inefficiency of their input/output (I/O) access patterns. Some recent work (e.g., C-trees and PaC-trees) focused on more I/O-friendly implementations of these algorithms. Surprisingly, however, there have been no results on bounding the I/O-costs for these algorithms. It remains open whether these algorithms can provide tight, provable guarantees in I/O-costs on trees.
This paper studies efficient parallel algorithms for set operations based on search tree algorithms using a join-based framework, with a special focus on achieving I/O efficiency in these algorithms. To better capture the I/O-efficiency in these algorithms in parallel, we introduce a new computational model, the Fork-Join I/O Model, to measure the I/O costs in fork-join parallelism. This model measures the total block transfers (I/O work) and their critical path (I/O span). Under this model, we propose our new solution based on B-trees. Our parallel algorithm computes the union, intersection, and difference of two B-trees with O(m log_B(n/m)) I/O work and O(log_B m ⋅ log₂ log_B n + log_B n) I/O span, where n and m ≤ n are the sizes of the two trees, and B is the block size.
Cite as
Michael T. Goodrich, Yan Gu, Ryuto Kitagawa, and Yihan Sun. Parallel Joinable B-Trees in the Fork-Join I/O Model. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 37:1-37:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{goodrich_et_al:LIPIcs.ISAAC.2025.37,
author = {Goodrich, Michael T. and Gu, Yan and Kitagawa, Ryuto and Sun, Yihan},
title = {{Parallel Joinable B-Trees in the Fork-Join I/O Model}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {37:1--37:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.37},
URN = {urn:nbn:de:0030-drops-249451},
doi = {10.4230/LIPIcs.ISAAC.2025.37},
annote = {Keywords: Parallel algorithm, I/O efficiency, search trees, B-trees}
}
Document
Structural Parameters for Steiner Orientation
Abstract
We consider the Steiner Orientation problem, where we are given as input a mixed graph G = (V,E,A) and a set of k demand pairs (s_i,t_i), i ∈ [k]. The goal is to orient the undirected edges of G in a way that the resulting directed graph has a directed path from s_i to t_i for all i ∈ [k]. We adopt the point of view of structural parameterized complexity and investigate the complexity of Steiner Orientation for standard measures, such as treewidth. Our results indicate that Steiner Orientation is a surprisingly hard problem from this point of view. In particular, our main contributions are the following:
1) We show that Steiner Orientation is NP-complete on instances where the underlying graph has feedback vertex number 2, treewidth 2, pathwidth 3, and vertex integrity 6.
2) We present an XP algorithm parameterized by vertex cover number vc of complexity n^O(vc²). Furthermore, we show that this running time is essentially optimal by proving that a running time of n^o(vc²) would refute the ETH.
3) We consider parameterizations by the number of undirected or directed edges (|E| or |A|) and we observe that the trivial 2^|E| n^O(1)-time algorithm for the former parameter is optimal under the SETH. Complementing this, we show that the problem admits a 2^O(|A|) n^O(1)-time algorithm.
In addition to the above, we consider the complexity of Steiner Orientation parameterized by tw+k (FPT), distance to clique (FPT), and vc+k (FPT with a polynomial kernel).
Cite as
Tesshu Hanaka, Michael Lampis, Nikolaos Melissinos, Edouard Nemery, Hirotaka Ono, and Manolis Vasilakis. Structural Parameters for Steiner Orientation. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 38:1-38:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{hanaka_et_al:LIPIcs.ISAAC.2025.38,
author = {Hanaka, Tesshu and Lampis, Michael and Melissinos, Nikolaos and Nemery, Edouard and Ono, Hirotaka and Vasilakis, Manolis},
title = {{Structural Parameters for Steiner Orientation}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {38:1--38:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.38},
URN = {urn:nbn:de:0030-drops-249461},
doi = {10.4230/LIPIcs.ISAAC.2025.38},
annote = {Keywords: ETH, Steiner Orientation, Treewidth}
}
Document
Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules
Abstract
In reconfiguration problems, we are given two feasible solutions to a graph problem and asked whether one can be transformed into the other via a sequence of feasible intermediate solutions under a given reconfiguration rule. While earlier work focused on modifying a single element at a time, recent studies have started examining how different rules impact computational complexity.
Motivated by recent progress, we study Independent Set Reconfiguration (ISR) and Vertex Cover Reconfiguration (VCR) under the k-Token Jumping (k-TJ) and k-Token Sliding (k-TS) models. In k-TJ, up to k vertices may be replaced, while k-TS additionally requires a perfect matching between removed and added vertices. It is known that the complexity of ISR crucially depends on k, ranging from PSPACE-complete and NP-complete to polynomial-time solvable.
In this paper, we further explore the gradient of computational complexity of the problems. We first show that ISR under k-TJ with k = |I| - μ remains NP-hard when μ is any fixed positive integer and the input graph is restricted to graphs of maximum degree 3 or planar graphs of maximum degree 4, where |I| is the size of feasible solutions. In addition, we prove that the problem belongs to NP not only for μ = O(1) but also for μ = O(log |I|). In contrast, we show that VCR under k-TJ is in XP when parameterized by μ = |S| - k, where |S| is the size of feasible solutions. Furthermore, we establish the PSPACE-completeness of ISR and VCR under both k-TJ and k-TS on several graph classes, for fixed k as well as superconstant k relative to the size of feasible solutions.
Cite as
Shuichi Hirahara, Naoto Ohsaka, Tatsuhiro Suga, Akira Suzuki, Yuma Tamura, and Xiao Zhou. Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{hirahara_et_al:LIPIcs.ISAAC.2025.39,
author = {Hirahara, Shuichi and Ohsaka, Naoto and Suga, Tatsuhiro and Suzuki, Akira and Tamura, Yuma and Zhou, Xiao},
title = {{Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {39:1--39:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.39},
URN = {urn:nbn:de:0030-drops-249474},
doi = {10.4230/LIPIcs.ISAAC.2025.39},
annote = {Keywords: combinatorial reconfiguration, extended reconfiguration rule, independent set reconfiguration, vertex cover reconfiguration, PSPACE-completeness, NP-completeness}
}
Document
Minimum Sum Coloring with Bundles in Trees and Bipartite Graphs
Abstract
The minimum sum coloring problem with bundles was introduced by Darbouy and Friggstad (SWAT 2024) as a common generalization of the minimum coloring problem and the minimum sum coloring problem. During their presentation, the following open problem was raised: whether the minimum sum coloring problem with bundles could be solved in polynomial time for trees. We answer their question in the negative by proving that the minimum sum coloring problem with bundles is NP-hard even for paths. We complement this hardness by providing algorithms of the following types. First, we provide a fixed-parameter algorithm for trees when the number of bundles is a parameter; this can be extended to graphs of bounded treewidth. Second, we provide a polynomial-time algorithm for trees when bundles form a partition of the vertex set and the difference between the number of vertices and the number of bundles is constant. Third, we provide a polynomial-time algorithm for trees when bundles form a partition of the vertex set and each bundle induces a connected subgraph. We further show that for bipartite graphs, the problem with weights is NP-hard even when the number of bundles is at least three, but is polynomial-time solvable when the number of bundles is at most two. The threshold shifts to three versus four for the problem without weights.
Cite as
Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto. Minimum Sum Coloring with Bundles in Trees and Bipartite Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 40:1-40:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{ito_et_al:LIPIcs.ISAAC.2025.40,
author = {Ito, Takehiro and Kakimura, Naonori and Kamiyama, Naoyuki and Kobayashi, Yusuke and Okamoto, Yoshio},
title = {{Minimum Sum Coloring with Bundles in Trees and Bipartite Graphs}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {40:1--40:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.40},
URN = {urn:nbn:de:0030-drops-249482},
doi = {10.4230/LIPIcs.ISAAC.2025.40},
annote = {Keywords: graph algorithms, minimum sum coloring, minimum coloring, fixed-parameter tractability, NP-hardness}
}
Document
A General Framework for Finding Diverse Solutions via Network Flow and Its Applications
Abstract
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find k solutions that maximize a specified diversity measure - the sum of pairwise Hamming distances or the size of the union of the k solutions. Our framework applies to problems satisfying two structural properties: (i) All solutions are of equal size and (ii) the family of all solutions can be represented by a surjection from the family of ideals of some finite poset. Under these conditions, we show that the problem of computing k diverse solutions can be reduced to the minimum cost flow problem and the maximum s-t flow problem. As applications, we demonstrate that both the unweighted minimum s-t cut problem and the stable matching problem satisfy the requirements of our framework. By utilizing the recent advances in network flows algorithms, we improve the previously known time complexities of the diverse problems, which were based on submodular function minimization.
Cite as
Yuni Iwamasa, Tomoki Matsuda, Shunya Morihira, and Hanna Sumita. A General Framework for Finding Diverse Solutions via Network Flow and Its Applications. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 41:1-41:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{iwamasa_et_al:LIPIcs.ISAAC.2025.41,
author = {Iwamasa, Yuni and Matsuda, Tomoki and Morihira, Shunya and Sumita, Hanna},
title = {{A General Framework for Finding Diverse Solutions via Network Flow and Its Applications}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {41:1--41:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.41},
URN = {urn:nbn:de:0030-drops-249492},
doi = {10.4230/LIPIcs.ISAAC.2025.41},
annote = {Keywords: Diverse Solutions, Network Flow Algorithm, Lattice Theory}
}
Document
Parameterized Reunion with Achromatic Number
Abstract
In this paper, we study the Achromatic Number problem. Given a graph G and an integer k, the task is to determine whether there exists a proper coloring of G, using at least k colors, in which every pair of distinct colors appears on the endpoints of some edge. It was established early on that the problem is fixed-parameter tractable (FPT)- even before the formal development of parameterized complexity. In fact, Farber, Hahn, Hell, and Miller [JCTB, 1986] devised an algorithm with a running time of 𝒪(f(k) ⋅ |E(G)|). Although the exact form of f(k) was not specified, it appears to be at least doubly exponential in k. In our work, we first present an algorithm with an explicit dependence on k, and then introduce another algorithm that is parameterized by the vertex cover number of the graph. More formally, we show the following.
- Achromatic Number is solvable in time 2^𝒪(k⁵)+𝒪(|E(G)|).
- Achromatic Number admits a polynomial kernel when the input is restricted to a d-degenerate graph and a more efficient kernel on trees.
- We also study the parameterized complexity of the problem with respect to Vertex Cover and show that it admits an FPT algorithm running in time 2^𝒪(𝓁²) ⋅ n^𝒪(1), where 𝓁 is the size of a vertex cover.
Cite as
Satyabrata Jana, Souvik Saha, Saket Saurabh, and Anannya Upasana. Parameterized Reunion with Achromatic Number. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 42:1-42:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{jana_et_al:LIPIcs.ISAAC.2025.42,
author = {Jana, Satyabrata and Saha, Souvik and Saurabh, Saket and Upasana, Anannya},
title = {{Parameterized Reunion with Achromatic Number}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {42:1--42:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.42},
URN = {urn:nbn:de:0030-drops-249502},
doi = {10.4230/LIPIcs.ISAAC.2025.42},
annote = {Keywords: Achromatic number, Coloring, Fixed-parameter tractability, Kernelization, Lower bound, W-hardness}
}
Document
New Approximate Distance Oracles and Their Applications
Abstract
Let G = (V, E) be an undirected graph with n vertices and m edges, and let μ = m/n. A distance oracle is a data structure designed to answer approximate distance queries, with the goal of achieving low stretch, efficient space usage, and fast query time. While much of the prior work focused on distance oracles with constant query time, this paper presents a comprehensive study of distance oracles with non-constant query time. We explore the tradeoffs between space, stretch, and query time of distance oracles in various regimes. Specifically, we consider both weighted and unweighted graphs in the regimes of stretch < 2 and stretch ≥ 2. In addition, we demonstrate several applications of our new distance oracles to the n-Pairs Shortest Paths (n-PSP) problem and the All Nodes Shortest Cycles (ANSC) problem. Our main contributions are:
- Weighted graphs: We present a new three-way trade-off between stretch, space, and query time, offering a natural extension of the classical Thorup–Zwick distance oracle [STOC’01 and JACM’05] to regimes with larger query time. Specifically, for any 0 < r < 1/2 and integer k ≥ 1, we construct a (2k(1 - 2r) - 1)-stretch distance oracle with Õ(m + n^{1 + 1/k}) space and Õ(μ n^r) query time. This construction provides an asymptotic improvement over the classical (2k - 1)-stretch and O(n^{1 + 1/k})-space tradeoff of Thorup and Zwick in sparse graphs, at the cost of increased query time. We also improve upon a result of Dalirrooyfard et al. [FOCS’22], who presented a (2k - 2)-stretch distance oracle with O(m + n^{1 + 1/k}) space and O(μ n^{1/k}) query time. In our oracle we reduce the stretch from (2k - 2) to (2k - 5) while preserving the same space and query time.
- Unweighted graphs: We present a (2k - 5, 4 + 2_{odd})-approximation distance oracle with O(n^{1 + 1/k}) space and O(n^{1/k}) query time. This improves upon a (2k - 2, 2_{odd})-approximation distance oracle of Dalirrooyfard et al. [FOCS’22] while maintaining the same space and query time. We also present a distance oracle that given u,v ∈ V returns an estimate d̂(u,v) ≤ d(u,v) + 2⌈ d(u,v) / 3 ⌉ + 2, using O(n^{4/3 + 2ε}) space and O(n^{1 - 3ε}) query time. To the best of our knowledge, this is the first distance oracle that simultaneously achieves a multiplicative stretch < 2, and a space complexity O(n^{1.5 - α}), for some α > 0.
- Applications for n-PSP and ANSC: We present an Õ(m^{1 - 1/(k+1)} n)-time algorithm for the n-PSP problem, that for every input pair ⟨s_i,t_i⟩, where i ∈ [n], returns an estimate d̂(s_i, t_i) such that d̂(s_i,t_i) ≤ d(s_i,t_i) + 2⌈d(s_i,t_i)/2k⌉. By allowing a small additive error, this result circumvents the conditional running time lower bound of Ω(m^{2 - 2/(k+1)} ⋅ n^{1/(k+1) - o(1)}), established by Dalirrooyfard et al. [FOCS’22] for achieving (1 + 1/k)-stretch. Additionally, we present an Õ(mn^{1 - 1/k})-time algorithm for the ANSC problem that computes, for every u ∈ V, an estimate ĉ_u such that ĉ_u ≤ SC(u) + 2⌈SC(u)/2(k - 1)⌉, where SC(u) denotes the length of the shortest cycle containing u. This improves upon the Õ(m^{2 - 2/k}n^{1/k})-time algorithm of Dalirrooyfard et al. [FOCS'22], while achieving the same approximation guarantee.
We obtain our results by developing several new techniques, among them are the borderline vertices technique and the middle vertex technique, which may be of independent interest.
Cite as
Avi Kadria and Liam Roditty. New Approximate Distance Oracles and Their Applications. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{kadria_et_al:LIPIcs.ISAAC.2025.43,
author = {Kadria, Avi and Roditty, Liam},
title = {{New Approximate Distance Oracles and Their Applications}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {43:1--43:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.43},
URN = {urn:nbn:de:0030-drops-249514},
doi = {10.4230/LIPIcs.ISAAC.2025.43},
annote = {Keywords: Distance oracles, Fine-grained algorithms, Graph algorithms, Data structures}
}
Document
Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio
Abstract
The Subset Sum Ratio problem (SSR) asks, given a multiset A of positive integers, to find two disjoint subsets of A such that the largest-to-smallest ratio of their sums is minimized. In this paper we study the k-version of SSR, namely k-Subset Sum Ratio (k-SSR), which asks to minimize the largest-to-smallest ratio of sums of k disjoint subsets of A. We develop an approximation scheme for k-SSR running in O(n^{2k}/ε^{k-1}) time, where n = |A| and ε is the error parameter. To the best of our knowledge, this is the first FPTAS for k-SSR for fixed k > 2.
We also study the k-way Number Partitioning Ratio (k-PART) problem, which differs from k-SSR in that the k subsets must constitute a partition of A; this problem in fact corresponds to the objective of minimizing the largest-to-smallest sum ratio in the family of Multiway Number Partitioning problems. We present a more involved FPTAS for k-PART, also achieving O(n^{2k}/ε^{k-1}) time complexity. Notably, k-PART is also equivalent to the Minimum Envy-Ratio problem with identical valuation functions, which has been studied in the context of fair division of indivisible goods. Thus, for the case of identical valuations, our FPTAS represents a significant improvement over the O(n^{4k²+1}/ε^{2k²}) bound obtained by Nguyen and Rothe’s FPTAS [Trung Thanh Nguyen and Jörg Rothe, 2014] for Minimum Envy-Ratio with general additive valuations.
Lastly, we propose a second FPTAS for k-SSR, which employs carefully designed calls to the first one; the new scheme has a time complexity of Õ(n/ε^{3k-1}), thus being much faster when n≫ 1/ ε.
Cite as
Sotiris Kanellopoulos, Giorgos Mitropoulos, Antonis Antonopoulos, Nikos Leonardos, Aris Pagourtzis, Christos Pergaminelis, Stavros Petsalakis, and Kanellos Tsitouras. Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 44:1-44:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{kanellopoulos_et_al:LIPIcs.ISAAC.2025.44,
author = {Kanellopoulos, Sotiris and Mitropoulos, Giorgos and Antonopoulos, Antonis and Leonardos, Nikos and Pagourtzis, Aris and Pergaminelis, Christos and Petsalakis, Stavros and Tsitouras, Kanellos},
title = {{Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {44:1--44:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.44},
URN = {urn:nbn:de:0030-drops-249521},
doi = {10.4230/LIPIcs.ISAAC.2025.44},
annote = {Keywords: Fully polynomial-time approximation schemes, Subset Sum Ratio, Number Partitioning, Fair division, Envy minimization, Pseudo-polynomial time algorithms}
}
Document
BFS and Reverse Shortest Paths for Ball Intersection Graphs in Three and Higher Dimensions
Abstract
Let ℬ be a collection of n arbitrary balls in ℝ³, and let G₀(ℬ) be their intersection graph. We provide an algorithm for performing BFS on G₀(ℬ), which runs in O^*(n^{4/3}) time, where the O^*(⋅) notation hides subpolynomial factors. For r ≥ 0, let G_r(ℬ) be the intersection graph of the set ℬ_r = {B+r ∣ B ∈ ℬ}, where B+r is the ball concentric with B whose radius is larger by r than the radius of B. We provide an efficient algorithm for the reverse shortest path (RSP) problem, where we are given two designated balls B_s, B_t of ℬ and a parameter 0 < λ < n, and seek the smallest value r^* for which G_{r^*}(ℬ) contains a path from B_s to B_t of at most λ edges. For the special case of congruent balls (equivalently, for points in ℝ³), the algorithm runs in O^*(n^{29/21}) ≈ O^*(n^{1.381}) time. For the general case, the algorithm runs in O^*(n^{56/39}) ≈ O^*(n^{1.436}) time. We also extend the technique to handle other measures of expansion and higher dimensions.
Cite as
Matthew J. Katz, Rachel Saban, and Micha Sharir. BFS and Reverse Shortest Paths for Ball Intersection Graphs in Three and Higher Dimensions. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 45:1-45:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{katz_et_al:LIPIcs.ISAAC.2025.45,
author = {Katz, Matthew J. and Saban, Rachel and Sharir, Micha},
title = {{BFS and Reverse Shortest Paths for Ball Intersection Graphs in Three and Higher Dimensions}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {45:1--45:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.45},
URN = {urn:nbn:de:0030-drops-249535},
doi = {10.4230/LIPIcs.ISAAC.2025.45},
annote = {Keywords: Computational geometry, reverse shortest paths, breadth-first search, shrink-and-bifurcate, intersection graphs}
}
Document
Realizing Metric Spaces with Convex Obstacles
Abstract
The presence of obstacles has a significant impact on distance computation, motion-planning, and visibility. These problems have been studied extensively in the planar setting, while our understanding of these problems in 3- and higher-dimensional spaces is still rudimentary. In this paper, we study the impact of different types of obstacles on the induced geodesic metric in 3-dimensional Euclidean space. We say that a finite metric space (X, dist_X) is approximately realizable by a collection 𝒯 of obstacles in ℝ³ if for any ε > 0 it can be embedded into (ℝ³⧵⋃_{T∈𝒯} T, dist_𝒯) with worst-case multiplicative distortion 1+ε, where dist_𝒯 denotes the geodesic distance in the free space induced by 𝒯. We focus on three key geometric properties of obstacles -convexity, disjointness, and fatness- and examine how dropping each one of them affects the existence of such embeddings.
Our main result concerns dropping the fatness property: we demonstrate that any finite metric space is realizable with 1+ε worst-case multiplicative distortion using a collection of convex and pairwise disjoint obstacles in ℝ³, even if the obstacles are congruent and equilateral triangles. Based on the same construction, we can also show that if we require fatness but drop any of the other two properties instead, then we can still approximately realize any finite metric space.
Our results have important implications on the approximability of tsp with obstacles, a natural variant of tsp introduced recently by Alkema et al. (ESA 2022). Specifically, we use the recent results of Banerjee et al. on tsp in doubling spaces (FOCS 2024) and of Chew et al. on distances among obstacles (Inf. Process. Lett. 2002) to show that tsp with obstacles admits a PTAS if the obstacles are convex, fat, and pairwise disjoint. If any of these three properties is dropped, then our results, combined with the APX-hardness of Metric tsp, demonstrate that tsp with obstacles is APX-hard.
Cite as
Sándor Kisfaludi-Bak and Leonidas Theocharous. Realizing Metric Spaces with Convex Obstacles. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 46:1-46:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{kisfaludibak_et_al:LIPIcs.ISAAC.2025.46,
author = {Kisfaludi-Bak, S\'{a}ndor and Theocharous, Leonidas},
title = {{Realizing Metric Spaces with Convex Obstacles}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {46:1--46:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.46},
URN = {urn:nbn:de:0030-drops-249545},
doi = {10.4230/LIPIcs.ISAAC.2025.46},
annote = {Keywords: traveling salesman, geodesic distance}
}
Document
Hardness and Fixed Parameter Tractability for Pinwheel Scheduling Problems
Abstract
In the Pinwheel Packing problem, we are given a set of recurring tasks, each associated with a positive integer a_i for task i. The objective is to select one task to perform each day such that every task i is performed at least once within every a_i consecutive days. The exact computational complexity of this problem, where ∑ 1/a_i = 1, has remained an open question for more than 30 years; in particular, it is still unknown whether the problem is NP-hard. The first contribution of this paper is to show that Pinwheel Packing cannot be solved in polynomial time under a standard complexity assumption, improving upon the hardness result shown by Jacobs and Longo. Additionally, we present fixed-parameter algorithms for variants of Pinwheel Packing, parameterized by the number of tasks.
Cite as
Yusuke Kobayashi and Bingkai Lin. Hardness and Fixed Parameter Tractability for Pinwheel Scheduling Problems. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 47:1-47:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{kobayashi_et_al:LIPIcs.ISAAC.2025.47,
author = {Kobayashi, Yusuke and Lin, Bingkai},
title = {{Hardness and Fixed Parameter Tractability for Pinwheel Scheduling Problems}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {47:1--47:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.47},
URN = {urn:nbn:de:0030-drops-249558},
doi = {10.4230/LIPIcs.ISAAC.2025.47},
annote = {Keywords: Pinwheel Scheduling, Polynomial-time Solvability, Packing and Covering, Fixed Parameter Algorithms}
}
Document
Quadratic Kernel for Cliques or Trees Vertex Deletion
Abstract
We consider Cliques or Trees Vertex Deletion, which is a hybrid of two fundamental parameterized problems: Cluster Vertex Deletion and Feedback Vertex Set. In this problem, we are given an undirected graph G and an integer k, and asked to find a vertex subset X of size at most k such that each connected component of G-X is either a clique or a tree. Jacob et al. (ISAAC, 2024) provided a kernel of O(k⁵) vertices for this problem, which was recently improved to O(k⁴) by Tsur (IPL, 2025).
Our main result is a kernel of O(k²) vertices. This result closes the gap between the kernelization result for Feedback Vertex Set, which corresponds to the case where each connected component of G-X must be a tree.
Although both cluster vertex deletion number and feedback vertex set number are well-studied structural parameters, little attention has been given to parameters that generalize both of them. In fact, the lowest common well-known generalization of them is clique-width, which is a highly general parameter. To fill the gap here, we initiate the study of the cliques or trees vertex deletion number as a structural parameter. We prove that Longest Cycle, which is a fundamental problem that does not admit o(n^k)-time algorithm unless ETH fails when k is the clique-width, becomes fixed-parameter tractable when parameterized by the cliques or trees vertex deletion number.
Cite as
Soh Kumabe. Quadratic Kernel for Cliques or Trees Vertex Deletion. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 48:1-48:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{kumabe:LIPIcs.ISAAC.2025.48,
author = {Kumabe, Soh},
title = {{Quadratic Kernel for Cliques or Trees Vertex Deletion}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {48:1--48:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.48},
URN = {urn:nbn:de:0030-drops-249568},
doi = {10.4230/LIPIcs.ISAAC.2025.48},
annote = {Keywords: Fixed-Parameter Tractability, Kernelization, Deletion to Scattered Graph Classes, Cluster Vertex Deletion, Feedback Vertex Set}
}
Document
Maximizing Social Welfare Among EF1 Allocations at the Presence of Two Types of Agents
Abstract
We study the fair allocation of indivisible items to n agents to maximize the utilitarian social welfare, where the fairness criterion is envy-free up to one item and there are only two different utility functions shared by the agents. We present a 2-approximation algorithm when the two utility functions are normalized, improving the previous best ratio of 16 √n shown for general normalized utility functions; thus this constant ratio approximation algorithm confirms the APX-completeness in this special case previously shown APX-hard. When there are only three agents, i.e., n = 3, the previous best ratio is 3 shown for general utility functions, and we present an improved and tight 5/3-approximation algorithm when the two utility functions are normalized, and a best possible and tight 2-approximation algorithm when the two utility functions are unnormalized.
Cite as
Jiaxuan Ma, Yong Chen, Guangting Chen, Mingyang Gong, Guohui Lin, and An Zhang. Maximizing Social Welfare Among EF1 Allocations at the Presence of Two Types of Agents. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 49:1-49:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{ma_et_al:LIPIcs.ISAAC.2025.49,
author = {Ma, Jiaxuan and Chen, Yong and Chen, Guangting and Gong, Mingyang and Lin, Guohui and Zhang, An},
title = {{Maximizing Social Welfare Among EF1 Allocations at the Presence of Two Types of Agents}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {49:1--49:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.49},
URN = {urn:nbn:de:0030-drops-249570},
doi = {10.4230/LIPIcs.ISAAC.2025.49},
annote = {Keywords: Fair allocation, utilitarian social welfare, envy-free up to one item, envy-cycle elimination, round robin, approximation algorithm}
}
Document
Matchgate Signatures Under Variable Permutations
Abstract
In this work, we introduce the concept of permutable matchgate signatures and leverage it to establish dichotomy theorems for #CSP and #R_D-CSP (D ≥ 3) on planar graphs without the variable ordering restriction. We also present a complete characterization of permutable matchgate signatures and their relationship to symmetric signatures. Besides, we give a sufficient and necessary condition for determining whether a matchgate signature retains its property under a certain variable permutation, which can be checked in polynomial time. In addition, we prove a dichotomy for Pl-#R_D-CSP (D ≥ 3), where the variable ordering restriction exists.
Cite as
Boning Meng and Yicheng Pan. Matchgate Signatures Under Variable Permutations. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{meng_et_al:LIPIcs.ISAAC.2025.50,
author = {Meng, Boning and Pan, Yicheng},
title = {{Matchgate Signatures Under Variable Permutations}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {50:1--50:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.50},
URN = {urn:nbn:de:0030-drops-249587},
doi = {10.4230/LIPIcs.ISAAC.2025.50},
annote = {Keywords: Computational Complexity, Matchgate Signature, Counting CSP}
}
Document
Distributed Complexity of P_k-Freeness: Decision and Certification
Abstract
The class of graphs that do not contain a path on k nodes as an induced subgraph (P_k-free graphs) has rich applications in the theory of graph algorithms. This paper explores the problem of deciding P_k-freeness from the viewpoint of distributed computing.
For specific small values of k, we present the first CONGEST algorithms specified for P_k-freeness, utilizing structural properties of P_k-free graphs in a novel way. Specifically, we show that P_k-freeness can be decided in Õ(1) rounds for k = 4 in the broadcast CONGEST model, and in Õ(n) rounds for k = 5 in the CONGEST model, where n is the number of nodes in the network and Õ(⋅) hides a polylog(n) factor. The main technical contribution is a novel technique used in our algorithm for P₅-freeness to distinguish induced 5-paths from non-induced ones, which is potentially applicable to other induced subgraphs. This technique also enables the construction of a local certification of P₅-freeness with certificates of size Õ(n). This improves Õ(n^{3/2}) by Bousquet and Zeitoun (TCS 2025), and is nearly optimal, given our Ω(n^{1-o(1)}) lower bound on certificate size.
For general k, we establish the first CONGEST lower bound, which is of the form n^{2-1/Θ(k)}. The n^{1/Θ(k)} factor is unavoidable, in view of the O(n^{2-2/(3k+2)}) upper bound by Eden et al. (Dist. Comp. 2022). Additionally, our approach yields the first superlinear lower bound on certificate size for local certification. This partially answers the conjecture on the optimal certificate size of P_k-freeness, asked by Bousquet et al. (arXiv:2402.12148).
Finally, we propose a novel variant of the problem called ordered P_k detection. We show that in the CONGEST model, the round complexity of ordered P_k detection is Ω̃(n) for k ≥ 5, and in contrast, proving any nontrivial lower bound for ordered P₃ detection implies a strong circuit lower bound. As a byproduct, we establish a circuit-complexity barrier for Ω(n^{1/2+ε}) quantum CONGEST lower bounds for induced 4-cycle detection. This is complemented by our Õ(n^{3/4}) quantum upper bound, which surpasses the classical Ω̃(n) lower bound by Le Gall and Miyamoto (ISAAC 2021).
Cite as
Masayuki Miyamoto. Distributed Complexity of P_k-Freeness: Decision and Certification. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 51:1-51:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{miyamoto:LIPIcs.ISAAC.2025.51,
author = {Miyamoto, Masayuki},
title = {{Distributed Complexity of P\underlinek-Freeness: Decision and Certification}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {51:1--51:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.51},
URN = {urn:nbn:de:0030-drops-249597},
doi = {10.4230/LIPIcs.ISAAC.2025.51},
annote = {Keywords: subgraph detection, CONGEST model, local certification}
}
Document
Local Routing on Ordered Θ-Graphs
Abstract
The problem of locally routing on geometric networks using limited memory is extensively studied in computational geometry. We consider one particular graph, the ordered Θ-graph, which is significantly harder to route on than the Θ-graph, for which a number of routing algorithms are known. Currently, no local routing algorithm is known for the ordered Θ-graph.
We prove that, unfortunately, there does not exist a deterministic memoryless local routing algorithm that works on the ordered Θ-graph. This motivates us to consider allowing a small amount of memory, and we present a deterministic O(1)-memory local routing algorithm that successfully routes from the source to the destination on the ordered Θ-graph. We show that our local routing algorithm converges to the destination in O(n) hops, where n is the number of vertices. To the best of our knowledge, our algorithm is the first deterministic local routing algorithm that is guaranteed to reach the destination on the ordered Θ-graph.
Cite as
André van Renssen and Shuei Sakaguchi. Local Routing on Ordered Θ-Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 52:1-52:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{vanrenssen_et_al:LIPIcs.ISAAC.2025.52,
author = {van Renssen, Andr\'{e} and Sakaguchi, Shuei},
title = {{Local Routing on Ordered \Theta-Graphs}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {52:1--52:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.52},
URN = {urn:nbn:de:0030-drops-249607},
doi = {10.4230/LIPIcs.ISAAC.2025.52},
annote = {Keywords: Ordered \Theta-graph, Local routing, Computational geometry}
}
Document
A Parameterized Study of Secluded Structures in Directed Graphs
Abstract
Given an undirected graph G and an integer k, the Secluded Π-Subgraph problem asks you to find a maximum size induced subgraph that satisfies a property Π and has at most k neighbors in the rest of the graph. This problem has been extensively studied; however, there is no prior study of the problem in directed graphs. This question has been mentioned by Jansen et al. [ISAAC'23].
In this paper, we initiate the study of Secluded Subgraph problems in directed graphs by incorporating different notions of neighborhoods: in-neighborhood, out-neighborhood, and their union. Formally, we call these problems {In, Out, Total}-Secluded Π-Subgraph, where given a directed graph G and an integer k, we want to find an induced subgraph satisfying Π of maximum size that has at most k in/out/total-neighbors in the rest of the graph, respectively. We investigate the parameterized complexity of these problems for different properties Π. In particular, we prove the following parameterized results:
- We design an FPT algorithm for the Total-Secluded Strongly Connected Subgraph problem when parameterized by k.
- We show that the Out-Secluded ℱ-Free Subgraph problem with parameter k is W[1]-hard, where ℱ is a family of directed graphs except any subgraph of a star graph whose edges are directed towards the center. This result also implies that In/Out-Secluded DAG is W[1]-hard, unlike the undirected variants of the two problems, which are FPT.
- We design an FPT-algorithm for In/Out/Total-Secluded α-Bounded Subgraph when parameterized by k, where α-bounded graphs are a superclass of tournaments.
- For undirected graphs, we improve the best-known FPT algorithm for Secluded Clique by providing a faster FPT algorithm that runs in time 1.6181^k n^𝒪(1).
Cite as
Jonas Schmidt, Shaily Verma, and Nadym Mallek. A Parameterized Study of Secluded Structures in Directed Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 53:1-53:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{schmidt_et_al:LIPIcs.ISAAC.2025.53,
author = {Schmidt, Jonas and Verma, Shaily and Mallek, Nadym},
title = {{A Parameterized Study of Secluded Structures in Directed Graphs}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {53:1--53:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.53},
URN = {urn:nbn:de:0030-drops-249616},
doi = {10.4230/LIPIcs.ISAAC.2025.53},
annote = {Keywords: Secluded Subgraph, Parametrized Complexity, Directed Graphs, Strong Connectivity}
}
Document
Reforming an Unfair Allocation by Exchanging Goods
Abstract
Fairly allocating indivisible goods is a frequently occurring task in everyday life. Given an initial allocation of the goods, we consider the problem of reforming it via a sequence of exchanges to attain fairness in the form of envy-freeness up to one good (EF1). We present a vast array of results on the complexity of determining whether it is possible to reach an EF1 allocation from the initial allocation and, if so, the minimum number of exchanges required. In particular, we uncover several distinctions based on the number of agents involved and their utility functions. Furthermore, we derive essentially tight bounds on the worst-case number of exchanges needed to achieve EF1.
Cite as
Sheung Man Yuen, Ayumi Igarashi, Naoyuki Kamiyama, and Warut Suksompong. Reforming an Unfair Allocation by Exchanging Goods. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 54:1-54:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{yuen_et_al:LIPIcs.ISAAC.2025.54,
author = {Yuen, Sheung Man and Igarashi, Ayumi and Kamiyama, Naoyuki and Suksompong, Warut},
title = {{Reforming an Unfair Allocation by Exchanging Goods}},
booktitle = {36th International Symposium on Algorithms and Computation (ISAAC 2025)},
pages = {54:1--54:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-408-6},
ISSN = {1868-8969},
year = {2025},
volume = {359},
editor = {Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.54},
URN = {urn:nbn:de:0030-drops-249626},
doi = {10.4230/LIPIcs.ISAAC.2025.54},
annote = {Keywords: fair division, indivisible goods, envy-freeness, exchanges}
}