55 Search Results for "Nagarajan, Viswanath"

Document
DOI: 10.4230/LIPIcs.STACS.2026.36
Time-Optimal Construction of String Synchronizing Sets

Authors: Jonas Ellert and Tomasz Kociumaka

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
A powerful design principle behind many modern string algorithms is local consistency: breaking the symmetry between string positions based on their small contexts so that matching fragments are handled consistently. Among the most influential instantiations of this principle are string synchronizing sets [Kempa & Kociumaka; STOC 2019]. A τ-synchronizing set of a string of length n is a set of O(n/τ) string positions, chosen using their length-2τ contexts, such that (outside of highly periodic regions) every block of τ consecutive positions contains at least one element of the set. Synchronizing sets have found dozens of applications in diverse settings, from quantum and dynamic algorithms to fully compressed computation. In the classic word RAM model, particularly for strings over small alphabets, they enabled faster solutions to core problems in data compression, text indexing, and string similarity. In this work, we show that any string T ∈ [0 .. σ)ⁿ can be preprocessed in O(n log σ / log n) time so that, for any given integer τ ∈ [1 .. n], a τ-synchronizing set of T can be constructed in O((n log τ)/(τ log n)) time. Both bounds are optimal in the word RAM model with machine word size w = Θ(log n), matching the information-theoretic minimum for the input and output sizes, respectively. Previously, constructing a τ-synchronizing set required O(n/τ) time after an O(n)-time preprocessing [Kociumaka, Radoszewski, Rytter, and Waleń; SICOMP 2024], or, in the restricted regime of τ < 0.2 log_σ n, without any preprocessing needed [Kempa & Kociumaka; STOC 2019]. A simple instantiation of our method outputs the synchronizing set as a sorted list in O(n/τ) time, or as a bitmask in O(n/log n) time. Our optimal construction produces a compact fully indexable dictionary, supporting select queries in O(1) time and rank queries in O(log ((log τ)/(log log n))) time. The latter complexity matches known unconditional cell-probe lower bounds for τ ≤ n^{1-Ω(1)}. To achieve this, we introduce a general framework for efficiently processing sparse integer sequences via a custom variable-length encoding. We also augment the optimal variant of van Emde Boas trees [Pătraşcu & Thorup; STOC 2006] with a deterministic linear-time construction. When the set is represented as a bitmask under our sparse encoding, the same guarantees for select and rank queries hold after preprocessing in time proportional to the size of our encoding (in words).
Cite as

Jonas Ellert and Tomasz Kociumaka. Time-Optimal Construction of String Synchronizing Sets. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ellert_et_al:LIPIcs.STACS.2026.36,
  author =	{Ellert, Jonas and Kociumaka, Tomasz},
  title =	{{Time-Optimal Construction of String Synchronizing Sets}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.36},
  URN =		{urn:nbn:de:0030-drops-255258},
  doi =		{10.4230/LIPIcs.STACS.2026.36},
  annote =	{Keywords: synchronizing sets, local consistency, packed strings}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.58
A Polylogarithmic Competitive Algorithm for Stochastic Online Sorting and TSP

Authors: Andreas Kalavas, Charalampos Platanos, and Thanos Tolias

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In Online Sorting, an array of n initially empty cells is given. At each time step t, an element x_t ∈ [0,1] arrives and must be irrevocably placed in an empty cell without knowledge of future arrivals. We aim to minimize the sum of absolute differences between pairs of elements placed in consecutive array cells, seeking an online placement strategy that results in a final array close to a sorted one. An interesting multidimensional generalization, referred to as the Online Traveling Salesperson Problem, arises when the request sequence consists of points in the d-dimensional unit cube and the objective is to minimize the sum of Euclidean distances between points in consecutive cells. Motivated by the recent work of (Abrahamsen, Bercea, Beretta, Klausen and Kozma; ESA 2024), we consider the stochastic version of Online Sorting (resp. Online TSP), where each element (resp. point) x_t is an i.i.d. sample from the uniform distribution on [0, 1] (resp. [0,1]^d). By carefully decomposing the request sequence into a hierarchy of balls-into-bins instances, where the balls to bins ratio is large enough so that bin occupancy is sharply concentrated around its mean and small enough so that we can efficiently deal with the elements placed in the same bin, we obtain an online algorithm that approximates the optimal cost within a factor of O(log² n) with high probability. Our result comprises an exponential improvement over the previously best known competitive ratio of Õ(n^{1/4}) for Stochastic Online Sorting due to (Abrahamsen et al.; ESA 2024) and O(√n) for (adversarial) Online TSP due to (Bertram, ESA 2025).
Cite as

Andreas Kalavas, Charalampos Platanos, and Thanos Tolias. A Polylogarithmic Competitive Algorithm for Stochastic Online Sorting and TSP. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 58:1-58:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kalavas_et_al:LIPIcs.STACS.2026.58,
  author =	{Kalavas, Andreas and Platanos, Charalampos and Tolias, Thanos},
  title =	{{A Polylogarithmic Competitive Algorithm for Stochastic Online Sorting and TSP}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{58:1--58:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.58},
  URN =		{urn:nbn:de:0030-drops-255473},
  doi =		{10.4230/LIPIcs.STACS.2026.58},
  annote =	{Keywords: sorting, online algorithm, balls-into-bins, TSP}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.31
Hamiltonicity Parameterized by Mim-Width Is (Indeed) Para-NP-Hard

Authors: Benjamin Bergougnoux and Lars Jaffke

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
We prove that Hamiltonian Path and Hamiltonian Cycle are NP-hard on graphs of linear mim-width 26, even when a linear order of the input graph with mim-width 26 is provided together with input. This fills a gap left by a broken proof of the para-NP-hardness of Hamiltonicity problems parameterized by mim-width.
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Benjamin Bergougnoux and Lars Jaffke. Hamiltonicity Parameterized by Mim-Width Is (Indeed) Para-NP-Hard. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 31:1-31:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bergougnoux_et_al:LIPIcs.IPEC.2025.31,
  author =	{Bergougnoux, Benjamin and Jaffke, Lars},
  title =	{{Hamiltonicity Parameterized by Mim-Width Is (Indeed) Para-NP-Hard}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{31:1--31:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.31},
  URN =		{urn:nbn:de:0030-drops-251631},
  doi =		{10.4230/LIPIcs.IPEC.2025.31},
  annote =	{Keywords: Hamiltonian Path, Hamiltonian Cycle, Mim-Width, Para-NP-Hardness}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.48
On the Roots of Independence Polynomial: Quantifying the Gap

Authors: Om Prakash and Vikram Sharma

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
The independence polynomial of a graph G is the generating polynomial corresponding to its independent sets of different sizes. More formally, if a_k(G) denotes the number of independent sets of G of size k then I(G,z) := ∑_k (-1)^k a_k(G) z^k. The study of evaluating I(G,z) has several deep connections to problems in combinatorics, complexity theory and statistical physics. Consequently, the roots of the independence polynomial have been studied in detail. In particular, many works have provided regions in the complex plane that are devoid of any roots of the polynomial. One of the first such results showed a lower bound on the absolute value of the smallest root β(G) of the polynomial. Furthermore, when G is connected, Goldwurm and Santini established that β(G) is a simple real root of I(G,z) smaller than one. An alternative proof was given by Csikvári. Both proofs do not provide a gap from β(G) to the smallest absolute value amongst all the other roots of I(G,z). In this paper, we quantify this gap.
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Om Prakash and Vikram Sharma. On the Roots of Independence Polynomial: Quantifying the Gap. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{prakash_et_al:LIPIcs.FSTTCS.2025.48,
  author =	{Prakash, Om and Sharma, Vikram},
  title =	{{On the Roots of Independence Polynomial: Quantifying the Gap}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{48:1--48:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.48},
  URN =		{urn:nbn:de:0030-drops-251281},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.48},
  annote =	{Keywords: Independence Polynomial, Root separation, Zero-free regions}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.19
Clustering in Varying Metrics

Authors: Deeparnab Chakrabarty, Jonathan Conroy, and Ankita Sarkar

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We introduce the aggregated clustering problem, where one is given T instances of a center-based clustering task over the same n points, but under different metrics. The goal is to open k centers to minimize an aggregate of the clustering costs - e.g., the average or maximum - where the cost is measured via k-center/median/means objectives. More generally, we minimize a norm Ψ over the T cost values. We show that for T ≥ 3, the problem is inapproximable to any finite factor in polynomial time. For T = 2, we give constant-factor approximations. We also show W[2]-hardness when parameterized by k, but obtain f(k,T)poly(n)-time 3-approximations when parameterized by both k and T. When the metrics have structure, we obtain efficient parameterized approximation schemes (EPAS). If all T metrics have bounded ε-scatter dimension, we achieve a (1+ε)-approximation in f(k,T,ε)poly(n) time. If the metrics are induced by edge weights on a common graph G of bounded treewidth tw, and Ψ is the sum function, we get an EPAS in f(T,ε,tw)poly(n,k) time. Conversely, unless (randomized) ETH is false, any finite factor approximation is impossible if parametrized by only T, even when the treewidth is tw = Ω(polylog n).
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Deeparnab Chakrabarty, Jonathan Conroy, and Ankita Sarkar. Clustering in Varying Metrics. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chakrabarty_et_al:LIPIcs.FSTTCS.2025.19,
  author =	{Chakrabarty, Deeparnab and Conroy, Jonathan and Sarkar, Ankita},
  title =	{{Clustering in Varying Metrics}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{19:1--19:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.19},
  URN =		{urn:nbn:de:0030-drops-251007},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.19},
  annote =	{Keywords: Clustering, approximation algorithms, LP rounding, parameterized and exact algorithms, dynamic programming, fixed parameter tractability, hardness of approximation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.20
Sparse Induced Subgraphs in P₇-Free Graphs of Bounded Clique Number

Authors: Maria Chudnovsky, Jadwiga Czyżewska, Kacper Kluk, Marcin Pilipczuk, and Paweł Rzążewski

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

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.
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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
DOI: 10.4230/LIPIcs.ISAAC.2025.13
Optimal Online Bipartite Matching in Degree-2 Graphs

Authors: Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

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.
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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
DOI: 10.4230/LIPIcs.GD.2025.21
On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers

Authors: Parinya Chalermsook, Ly Orgo, and Minoo Zarsav

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
This paper considers the Zarankiewicz problem in bipartite graphs with low-dimensional geometric representation (i.e., low Ferrers dimension). Let Z(n;k) be the maximum number of edges in a bipartite graph with n nodes and is free of a k-by-k biclique. Note that Z(n;k) ∈ Ω(nk) for all "natural" graph classes. Our first result reveals a separation between bipartite graphs of Ferrers dimension three and four: while we show that Z(n;k) ≤ 9n(k-1) for graphs of Ferrers dimension three, Z(n;k) ∈ Ω(n k ⋅ (log n)/(log log n)) for Ferrers dimension four graphs (Chan & Har-Peled, 2023) (Chazelle, 1990). To complement this, we derive a tight upper bound of 2n(k-1) for chordal bipartite graphs and 54n(k-1) for grid intersection graphs (GIG), a prominent graph class residing in four Ferrers dimensions and capturing planar bipartite graphs as well as bipartite intersection graphs of rectangles. Previously, the best-known bound for GIG was Z(n;k) ∈ O(2^{O(k)} n), implied by the results of Fox & Pach (2006) and Mustafa & Pach (2016). Our results advance and offer new insights into the interplay between Ferrers dimensions and extremal combinatorics.
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Parinya Chalermsook, Ly Orgo, and Minoo Zarsav. On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 21:1-21:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chalermsook_et_al:LIPIcs.GD.2025.21,
  author =	{Chalermsook, Parinya and Orgo, Ly and Zarsav, Minoo},
  title =	{{On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{21:1--21:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.21},
  URN =		{urn:nbn:de:0030-drops-250074},
  doi =		{10.4230/LIPIcs.GD.2025.21},
  annote =	{Keywords: Bipartite graph classes, extremal graph theory, geometric intersection graphs, Zarankiewicz problem, bicliques}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.37
Towards Optimal Distributed Edge Coloring with Fewer Colors

Authors: Manuel Jakob, Yannic Maus, and Florian Schager

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
There is a huge difference in techniques and runtimes of distributed algorithms for problems that can be solved by a sequential greedy algorithm and those that cannot. A prime example of this contrast appears in the edge coloring problem: while (2Δ-1)-edge coloring - where Δ is the maximum degree - can be solved in 𝒪(log^{∗}(n)) rounds on constant-degree graphs, the seemingly minor reduction to (2Δ-2) colors leads to an Ω(log n) lower bound [Chang, He, Li, Pettie & Uitto, SODA'18]. Understanding this sharp divide between very local problems and inherently more global ones remains a central open question in distributed computing and it is a core focus of this paper. As our main contribution we design a deterministic distributed 𝒪(log n)-round reduction from the (2Δ-2)-edge coloring problem to the much easier (2Δ-1)-edge coloring problem. This reduction is optimal, as the (2Δ-2)-edge coloring problem admits an Ω(log n) lower bound that even holds on the class of constant-degree graphs, whereas the 2Δ-1-edge coloring problem can be solved in 𝒪(log^{∗}n) rounds. By plugging in the (2Δ-1)-edge coloring algorithms from [Balliu, Brandt, Kuhn & Olivetti, PODC'22] running in 𝒪(log^{12}Δ + log^{∗} n) rounds, we obtain an optimal runtime of 𝒪(log n) rounds as long as Δ = 2^{𝒪(log^{1/12} n)}. Previously, such an optimal algorithm was only known for the class of constant-degree graphs [Brandt, Maus, Narayanan, Schager & Uitto, SODA'25]. Furthermore, on general graphs our reduction improves the runtime from 𝒪̃(log³ n) to 𝒪̃(log^{5/3} n). In addition, we also obtain an optimal 𝒪(log log n)-round randomized reduction of (2Δ - 2)-edge coloring to (2Δ - 1)-edge coloring. This leads to a 𝒪̃(log^{5/3} log n)-round (2Δ-2)-edge coloring algorithm, which beats the (very recent) previous state-of-the-art taking 𝒪̃(log^{8/3}log n) rounds from [Bourreau, Brandt & Nolin, STOC'25]. Lastly, we obtain an 𝒪(log_Δ n)-round reduction from the (2Δ-1)-edge coloring, albeit to the somewhat harder maximal independent set (MIS) problem.
Cite as

Manuel Jakob, Yannic Maus, and Florian Schager. Towards Optimal Distributed Edge Coloring with Fewer Colors. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 37:1-37:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jakob_et_al:LIPIcs.DISC.2025.37,
  author =	{Jakob, Manuel and Maus, Yannic and Schager, Florian},
  title =	{{Towards Optimal Distributed Edge Coloring with Fewer Colors}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{37:1--37:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.37},
  URN =		{urn:nbn:de:0030-drops-248547},
  doi =		{10.4230/LIPIcs.DISC.2025.37},
  annote =	{Keywords: distributed graph algorithms, edge coloring, LOCAL model}
}
Document
DOI: 10.4230/DagRep.15.3.159
Approximation Algorithms for Stochastic Optimization (Dagstuhl Seminar 25132)

Authors: Lisa Hellerstein, Viswanath Nagarajan, and Kevin Schewior

Published in: Dagstuhl Reports, Volume 15, Issue 3 (2025)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 25132 "Approximation Algorithms for Stochastic Optimization". In this seminar, we gathered researchers from different areas interested in combinatorial optimization problems in which there is some stochasticity in the input. The focus was on approximation algorithms for computing adaptive or non-adaptive strategies to interact with this stochastic uncertainty as well as structural measures such as the adaptivity gap.
Cite as

Lisa Hellerstein, Viswanath Nagarajan, and Kevin Schewior. Approximation Algorithms for Stochastic Optimization (Dagstuhl Seminar 25132). In Dagstuhl Reports, Volume 15, Issue 3, pp. 159-176, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{hellerstein_et_al:DagRep.15.3.159,
  author =	{Hellerstein, Lisa and Nagarajan, Viswanath and Schewior, Kevin},
  title =	{{Approximation Algorithms for Stochastic Optimization (Dagstuhl Seminar 25132)}},
  pages =	{159--176},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2025},
  volume =	{15},
  number =	{3},
  editor =	{Hellerstein, Lisa and Nagarajan, Viswanath and Schewior, Kevin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.15.3.159},
  URN =		{urn:nbn:de:0030-drops-248959},
  doi =		{10.4230/DagRep.15.3.159},
  annote =	{Keywords: adaptivity, approximation algorithms, combinatorial optimization, stochastic optimization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.98
Fine-Grained Classification of Detecting Dominating Patterns

Authors: Jonathan Dransfeld, Marvin Künnemann, and Mirza Redzic

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We consider the following generalization of dominating sets: Let G be a host graph and P be a pattern graph P. A dominating P-pattern in G is a subset S of vertices in G that (1) forms a dominating set in G and (2) induces a subgraph isomorphic to P. The graph theory literature studies the properties of dominating P-patterns for various patterns P, including cliques, matchings, independent sets, cycles and paths. Previous work (Kunnemann, Redzic 2024) obtains algorithms and conditional lower bounds for detecting dominating P-patterns particularly for P being a k-clique, a k-independent set and a k-matching. Their results give conditionally tight lower bounds if k is sufficiently large (where the bound depends the matrix multiplication exponent ω). We ask: Can we obtain a classification of the fine-grained complexity for all patterns P? Indeed, we define a graph parameter ρ(P) such that if ω = 2, then (n^ρ(P) m^{(|V(P)|-ρ(P))/2})^{1±o(1)} is the optimal running time assuming the Orthogonal Vectors Hypothesis, for all patterns P except the triangle K₃. Here, the host graph G has n vertices and m = Θ(n^α) edges, where 1 ≤ α ≤ 2. The parameter ρ(P) is closely related (but sometimes different) to a parameter δ(P) = max_{S ⊆ V(P)} |S|-|N(S)| studied in (Alon 1981) to tightly quantify the maximum number of occurrences of induced subgraphs isomorphic to P. Our results stand in contrast to the lack of a full fine-grained classification of detecting an arbitrary (not necessarily dominating) induced P-pattern.
Cite as

Jonathan Dransfeld, Marvin Künnemann, and Mirza Redzic. Fine-Grained Classification of Detecting Dominating Patterns. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 98:1-98:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dransfeld_et_al:LIPIcs.ESA.2025.98,
  author =	{Dransfeld, Jonathan and K\"{u}nnemann, Marvin and Redzic, Mirza},
  title =	{{Fine-Grained Classification of Detecting Dominating Patterns}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{98:1--98:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.98},
  URN =		{urn:nbn:de:0030-drops-245679},
  doi =		{10.4230/LIPIcs.ESA.2025.98},
  annote =	{Keywords: fine-grained complexity theory, domination in graphs, subgraph isomorphism, classification theorem, parameterized algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.79
Semi-Streaming Algorithms for Hypergraph Matching

Authors: Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We propose two one-pass streaming algorithms for the NP-hard hypergraph matching problem. The first algorithm stores a small subset of potential matching edges in a stack using dual variables to select edges. It has an approximation guarantee of 1/(d(1+ε)) and requires 𝒪((n/ε)log²n) bits of memory, where n is the number of vertices in the hypergraph, d is the maximum number of vertices in a hyperedge, and ε > 0 is a parameter to be chosen. The second algorithm computes, stores, and updates a single matching as the edges stream, with an approximation ratio dependent on a parameter α. Its best approximation guarantee is 1/((2d-1) + 2 √{d(d-1)}), and it requires only 𝒪(n) memory. We have implemented both algorithms and compared them with respect to solution quality, memory consumption, and running times on two diverse sets of hypergraphs with a non-streaming greedy and a naive streaming algorithm. Our results show that the streaming algorithms achieve much better solution quality than naive algorithms when facing adverse orderings. Furthermore, these algorithms reduce the memory required by a factor of 13 in the geometric mean on our test problems, and also outperform the offline Greedy algorithm in running time.
Cite as

Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz. Semi-Streaming Algorithms for Hypergraph Matching. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{reinstadtler_et_al:LIPIcs.ESA.2025.79,
  author =	{Reinst\"{a}dtler, Henrik and Ferdous, S M and Pothen, Alex and U\c{c}ar, Bora and Schulz, Christian},
  title =	{{Semi-Streaming Algorithms for Hypergraph Matching}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{79:1--79:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.79},
  URN =		{urn:nbn:de:0030-drops-245478},
  doi =		{10.4230/LIPIcs.ESA.2025.79},
  annote =	{Keywords: hypergraph, matching, semi-streaming}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.70
Improved Parallel Derandomization via Finite Automata with Applications

Authors: Jeff Giliberti and David G. Harris

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A central approach to algorithmic derandomization is the construction of small-support probability distributions that "fool” randomized algorithms, often enabling efficient parallel (NC) implementations. An abstraction of this idea is fooling polynomial-space statistical tests computed via finite automata [Sivakumar STOC'02]; this encompasses a wide range of properties including k-wise independence and sums of random variables. We present new parallel algorithms to fool finite-state automata, with significantly reduced processor complexity. Briefly, our approach is to iteratively sparsify distributions using a work-efficient lattice rounding routine and maintain accuracy by tracking an aggregate weighted error that is determined by the Lipschitz value of the statistical tests being fooled. We illustrate with improved applications to the Gale-Berlekamp Switching Game and to approximate MAX-CUT via SDP rounding. These involve further several optimizations, such as the truncation of the state space of the automata and FFT-based convolutions to compute transition probabilities efficiently.
Cite as

Jeff Giliberti and David G. Harris. Improved Parallel Derandomization via Finite Automata with Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 70:1-70:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{giliberti_et_al:LIPIcs.ESA.2025.70,
  author =	{Giliberti, Jeff and Harris, David G.},
  title =	{{Improved Parallel Derandomization via Finite Automata with Applications}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{70:1--70:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.70},
  URN =		{urn:nbn:de:0030-drops-245381},
  doi =		{10.4230/LIPIcs.ESA.2025.70},
  annote =	{Keywords: Parallel Algorithms, Derandomization, MAX-CUT, Gale-Berlekamp Switching Game}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.80
Online Metric TSP

Authors: Christian Bertram

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
In the online metric traveling salesperson problem, n points of a metric space arrive one by one and have to be placed (immediately and irrevocably) into empty cells of a size-n array. The goal is to minimize the sum of distances between consecutive points in the array. This problem was introduced by Abrahamsen, Bercea, Beretta, Klausen, and Kozma [ESA'24] as a generalization of the online sorting problem, which was introduced by Aamand, Abrahamsen, Beretta, and Kleist [SODA'23] as a tool in their study of online geometric packing problems. Online metric TSP has been studied for a range of fixed metric spaces. For 1-dimensional Euclidean space, the problem is equivalent to online sorting, where an optimal competitive ratio of Θ(√n) is known. For d-dimensional Euclidean space, the best-known upper bound is O(2^d √{dn log n}), leaving a gap to the Ω(√n) lower bound. Finally, for the uniform metric, where all distances are 0 or 1, the optimal competitive ratio is known to be Θ(log n). We study the problem for a general metric space, presenting an algorithm with competitive ratio O(√n). In particular, we close the gap for d-dimensional Euclidean space, completely removing the dependence on dimension. One might hope to simultaneously guarantee competitive ratio O(√n) in general and O(log n) for the uniform metric, but we show that this is impossible.
Cite as

Christian Bertram. Online Metric TSP. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 80:1-80:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bertram:LIPIcs.ESA.2025.80,
  author =	{Bertram, Christian},
  title =	{{Online Metric TSP}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{80:1--80:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.80},
  URN =		{urn:nbn:de:0030-drops-245485},
  doi =		{10.4230/LIPIcs.ESA.2025.80},
  annote =	{Keywords: online algorithm, metric space, TSP}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.16
On Algorithmic Applications of ℱ-Branchwidth

Authors: Benjamin Bergougnoux, Thekla Hamm, Lars Jaffke, and Paloma T. Lima

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
F-branchwidth is a framework for width measures of graphs, recently introduced by Eiben et al. [ITCS 2022], that captures tree-width, co-tree-width, clique-width, and mim-width, and several of their generalizations and interpolations. In this work, we search for algorithmic applications of F-branchwidth measures that do not have an equivalent counterpart in the literature so far. Our first contribution is a minimal set of eleven F-branchwidth measures such that each of the infinitely many F-branchwidth measures is equivalent to one of the eleven. We observe that for the FO Model Checking problem, each F-branchwidth is either equivalent to clique-width (and therefore has an FPT-algorithm by formula length plus the width) or the problem remains as hard as on general graphs even on graphs of constant width. Next, we study the number of equivalence classes of the neighborhood equivalence in a decomposition, which upper bounds the run time of the model checking algorithm for ACDN logic recently introduced by Bergougnoux et al. [SODA 2023]. We give structural lower bounds that show that for each F-branchwidth, an efficient model checking algorithm was already known or cannot be obtained via this method. Lastly, we classify the complexity of Independent Set parameterized by any F-branchwidth except for one open case. Also here, our contributions are lower bounds. In this context, we also prove that Independent Set on graphs of mim-width w cannot be solved in time n^o(w) unless the Exponential Time Hypothesis fails, answering an open question in the literature.
Cite as

Benjamin Bergougnoux, Thekla Hamm, Lars Jaffke, and Paloma T. Lima. On Algorithmic Applications of ℱ-Branchwidth. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bergougnoux_et_al:LIPIcs.ESA.2025.16,
  author =	{Bergougnoux, Benjamin and Hamm, Thekla and Jaffke, Lars and Lima, Paloma T.},
  title =	{{On Algorithmic Applications of ℱ-Branchwidth}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.16},
  URN =		{urn:nbn:de:0030-drops-244849},
  doi =		{10.4230/LIPIcs.ESA.2025.16},
  annote =	{Keywords: Graph width parameters, parameterized complexity, F-branchwidth, tree-width, clique-width, rank-width, mim-width, FO model checking, DN logic, Independent Set, ETH}
}
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