Volume
LIPIcs, Volume 349
19th International Symposium on Algorithms and Data Structures (WADS 2025)
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Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Algorithms and Data Structures Symposium (WADS)
Publication Details
- published at: 2025-08-29
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-398-0
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Complete Volume
LIPIcs, Volume 349, WADS 2025, Complete Volume
Abstract
LIPIcs, Volume 349, WADS 2025, Complete Volume
Cite as
19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 1-882, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@Proceedings{morin_et_al:LIPIcs.WADS.2025,
title = {{LIPIcs, Volume 349, WADS 2025, Complete Volume}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {1--882},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025},
URN = {urn:nbn:de:0030-drops-245905},
doi = {10.4230/LIPIcs.WADS.2025},
annote = {Keywords: LIPIcs, Volume 349, WADS 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
19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{morin_et_al:LIPIcs.WADS.2025.0,
author = {Morin, Pat and Oh, Eunjin},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {0:i--0:xviii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.0},
URN = {urn:nbn:de:0030-drops-245890},
doi = {10.4230/LIPIcs.WADS.2025.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
Constructing and Routing on Geometric Spanners (Invited Talk)
Abstract
A geometric graph G = (V,E) is a graph whose vertex set V is a set of points in the plane and whose edge set E is a set of segments joining vertices. Typically, the edges are weighted with the Euclidean distance between their endpoints and we refer to such graphs as Euclidean geometric graphs. A spanning subgraph H of a Euclidean geometric graph G is a t-spanner of G provided that for every edge xy ∈ G, the shortest path between x and y in H has weight that is no more than t times the weight of the edge xy. The smallest constant t for which H is a t-spanner of G is its spanning ratio.
An online routing algorithm A is an algorithm that finds a short path in a graph without having full knowledge of the graph. The routing ratio of A is analogous to the spanning ratio except that the ratio is with respect to the weight of the path followed by the routing algorithm as opposed to the shortest path. Thus, the routing ratio, by definition, is an upper bound on the spanning ratio.
In this talk, we will review results and present open problems on different variants of the problem of constructing and routing on geometric t-spanners.
Cite as
Prosenjit Bose. Constructing and Routing on Geometric Spanners (Invited Talk). In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bose:LIPIcs.WADS.2025.1,
author = {Bose, Prosenjit},
title = {{Constructing and Routing on Geometric Spanners}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {1:1--1:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.1},
URN = {urn:nbn:de:0030-drops-242320},
doi = {10.4230/LIPIcs.WADS.2025.1},
annote = {Keywords: Geometric Spanners, Local Routing Algorithms}
}
Document
Invited Talk
Unintuitive Facts About Distances on Planar Graphs (Invited Talk)
Abstract
Conventional wisdom told us that planar graphs are essentially edge-weighted grids, with more or less equal side-lengths. An n-node n^{1/2}-by-n^{1/2} square grid has treewidth Θ(n^{1/2}); and if we want to preserve shortest-path distances between every pair of boundary nodes, intuitively we have to keep all the n^{1/2} column and row paths, which together create n "crossings" that cannot be removed. This seems to suggest that planar graphs are incompressible and not tree-like. Or does it?
In this talk we will discuss three unintuitive, and perhaps surprising, facts about planar metrics in the (1+ε)-approximation regime. First we demonstrate how to construct emulator for planar graphs that preserves all-pair distances between k terminals, and has size Õ_ε(k). (This implies, for the grid example above, the resulting emulator has size Õ(n^{1/2}).)
Second, planar metrics can be covered using constantly(!) many trees, in the sense that we can construct O(1) many trees independent to the size of the input graph that never shrinks distances, so that given any pair of nodes x and y, there is one tree T that contains both x and y whose distance on T is stretched by at most a 1+ε factor. Along the way we will introduce a novel structure on planar metrics - the gridtrees - that enables such tree covers, as well as its applications in the resolution to the Steiner point removal problem, and in constructing embeddings of planar graphs into polylog-treewidth graphs with (1+ε)-distortion. (Which means, if we are willing to distort the distance by a small amount, planar metrics are very much tree-like.)
Finally, we will discuss the issue of spanning. Both results above rely on the fact that the emulator and the tree cover use "Steiner nodes", which are nodes not presented in the original input graph. Maybe this is cheating, and the distance compression is only possible because of these nodes that appear out of nowhere? Our goal is to convince you otherwise: We can in fact construct emulators for planar graphs that are minors, which only uses paths and edges from the input planar graph; and in the case of tree covers, we are one or two new structures away from enforcing the trees to be spanning, that is, the edges in the trees have come from the input graph as well.
Cite as
Hsien-Chih Chang. Unintuitive Facts About Distances on Planar Graphs (Invited Talk). In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{chang:LIPIcs.WADS.2025.2,
author = {Chang, Hsien-Chih},
title = {{Unintuitive Facts About Distances on Planar Graphs}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {2:1--2:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.2},
URN = {urn:nbn:de:0030-drops-242338},
doi = {10.4230/LIPIcs.WADS.2025.2},
annote = {Keywords: planar, emulator, tree cover, gridtree, spanning, sparsifier, tree embedding, clustering, Baker's technique, KPR decomposition, low-diameter decomposition, quadtree, shortest-path separator, portal}
}
Document
Support Vector Machines in the Hilbert Geometry
Abstract
Support Vector Machines (SVMs) are a class of classification models in machine learning that are based on computing a maximum-margin separator between two sets of points. The SVM problem has been heavily studied for Euclidean geometry and for a number of kernels. In this paper, we consider the linear SVM problem in the Hilbert metric, a non-Euclidean geometry defined over a convex body. We present efficient algorithms for computing the SVM classifier for a set of n points in the Hilbert metric defined by convex polygons in the plane and convex polytopes in d-dimensional space. We also consider the problems in the related Funk distance.
Cite as
Aditya Acharya, Auguste H. Gezalyan, Julian Vanecek, David M. Mount, and Sunil Arya. Support Vector Machines in the Hilbert Geometry. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{acharya_et_al:LIPIcs.WADS.2025.3,
author = {Acharya, Aditya and Gezalyan, Auguste H. and Vanecek, Julian and Mount, David M. and Arya, Sunil},
title = {{Support Vector Machines in the Hilbert Geometry}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {3:1--3:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.3},
URN = {urn:nbn:de:0030-drops-242348},
doi = {10.4230/LIPIcs.WADS.2025.3},
annote = {Keywords: Support vector machines, Hilbert geometry, linear classification, machine learning, LP-type problems}
}
Document
Evolving Distributions Under Local Motion
Abstract
Geometric data sets that arise in modern applications are often very large and change dynamically over time. A popular framework for dealing with such data sets is the evolving data framework, where a discrete structure continuously varies over time due to the unseen actions of an evolver, which makes small changes to the data. An algorithm probes the current state through an oracle, and the objective is to maintain a hypothesis of the data set’s current state that is close to its actual state at all times. In this paper, we apply this framework to maintaining a set of n point objects in motion in d-dimensional Euclidean space. To model the uncertainty in the object locations, both the ground truth and hypothesis are based on spatial probability distributions, and the distance between them is measured by the Kullback-Leibler divergence (relative entropy). We introduce a simple and intuitive motion model in which, with each time step, the distance that any object can move is a fraction of the distance to its nearest neighbor. We present an algorithm that, in steady state, guarantees a distance of O(n) between the true and hypothesized placements. We also show that for any algorithm in this model, there is an evolver that can generate a distance of Ω(n), implying that our algorithm is asymptotically optimal.
Cite as
Aditya Acharya and David M. Mount. Evolving Distributions Under Local Motion. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{acharya_et_al:LIPIcs.WADS.2025.4,
author = {Acharya, Aditya and Mount, David M.},
title = {{Evolving Distributions Under Local Motion}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {4:1--4:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.4},
URN = {urn:nbn:de:0030-drops-242357},
doi = {10.4230/LIPIcs.WADS.2025.4},
annote = {Keywords: Evolving data, tracking, imprecise points, local-motion model, online algorithms}
}
Document
On Planar Straight-Line Dominance Drawings
Abstract
We study the following question, which has been considered since the 90’s: Does every st-planar graph admit a planar straight-line dominance drawing? We show concrete evidence for the difficulty of this question, by proving that, unlike upward planar straight-line drawings, planar straight-line dominance drawings with prescribed y-coordinates do not always exist and planar straight-line dominance drawings cannot always be constructed via a contract-draw-expand inductive approach. We also show several classes of st-planar graphs that always admit a planar straight-line dominance drawing. These include st-planar 3-trees in which every stacking operation introduces two edges incoming into the new vertex, st-planar graphs in which every vertex is adjacent to the sink, and st-planar graphs in which no face has the left boundary that is a single edge.
Cite as
Patrizio Angelini, Michael A. Bekos, Giuseppe Di Battista, Fabrizio Frati, Luca Grilli, and Giacomo Ortali. On Planar Straight-Line Dominance Drawings. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{angelini_et_al:LIPIcs.WADS.2025.5,
author = {Angelini, Patrizio and Bekos, Michael A. and Di Battista, Giuseppe and Frati, Fabrizio and Grilli, Luca and Ortali, Giacomo},
title = {{On Planar Straight-Line Dominance Drawings}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {5:1--5:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.5},
URN = {urn:nbn:de:0030-drops-242361},
doi = {10.4230/LIPIcs.WADS.2025.5},
annote = {Keywords: st-graphs, dominance drawings, planar straight-line drawings, upward planarity}
}
Document
Vantage Point Selection Algorithms for Bottleneck Capacity Estimation
Abstract
Motivated by the problem of estimating bottleneck capacities on the Internet, we formulate and study the problem of vantage point selection. We are given a graph G = (V, E) whose edges E have unknown capacity values that are to be discovered. Probes from a vantage point, i.e, a vertex v ∈ V, along shortest paths from v to all other vertices, reveal bottleneck edge capacities along each path. Our goal is to select k vantage points from V that reveal the maximum number of bottleneck edge capacities.
We consider both a non-adaptive setting where all k vantage points are selected before any bottleneck capacity is revealed, and an adaptive setting where each vantage point selection instantly reveals bottleneck capacities along all shortest paths starting from that point. In the non-adaptive setting, by considering a relaxed model where edge capacities are drawn from a random permutation (which still leaves the problem of maximizing the expected number of revealed edges NP-hard), we are able to give a 1-1/e approximate algorithm. In the adaptive setting we work with the least permissive model where edge capacities are arbitrarily fixed but unknown. We compare with the best solution for the particular input instance (i.e. by enumerating all choices of k tuples), and provide both lower bounds on instance optimal approximation algorithms and upper bounds for trees and planar graphs.
Cite as
Vikrant Ashvinkumar, Rezaul Chowdhury, Jie Gao, Mayank Goswami, Joseph S. B. Mitchell, and Valentin Polishchuk. Vantage Point Selection Algorithms for Bottleneck Capacity Estimation. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{ashvinkumar_et_al:LIPIcs.WADS.2025.6,
author = {Ashvinkumar, Vikrant and Chowdhury, Rezaul and Gao, Jie and Goswami, Mayank and Mitchell, Joseph S. B. and Polishchuk, Valentin},
title = {{Vantage Point Selection Algorithms for Bottleneck Capacity Estimation}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {6:1--6:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.6},
URN = {urn:nbn:de:0030-drops-242376},
doi = {10.4230/LIPIcs.WADS.2025.6},
annote = {Keywords: Bottleneck capacity, Approximation algorithms, Instance optimality}
}
Document
Approximation and Parameterized Algorithms for Covering with Disks of Two Types of Radii
Abstract
We study the Discrete Covering with Two Types of Radii problem motivated by its application in wireless networks. In this problem, the goal is to assign either small-range high frequency or large-range low frequency to each access point, maximizing the number of users in high-frequency regions while ensuring that each user is in the range of an access point. Unlike other weighted covering problems, our problem requires satisfying two simultaneous objectives, which calls for novel approaches that leverage the underlying geometry of the problem. In our work, we present two new algorithms: the first is a polynomial-time (2.5 + ε)-approximation, and the second is an exact algorithm for sparse instances, which is fixed-parameter tractable (FPT) in the number of large-radius disks. We also prove that such an FPT algorithm is impossible for general instances lacking sparsity, assuming the Exponential Time Hypothesis. Before our work, the best-known polynomial-time approximation factor was 4 for the problem.
Our approximation algorithm results from a fine-grained classification of points that can contribute to the gain of a solution. Based on this classification, we design two sub-algorithms with interdependent guarantees to recover the respective class of points as gain. Our algorithm exploits further properties of Delaunay triangulations to achieve the improved bound. The FPT algorithm is based on branching that utilizes the sparsity of the instances to limit the overall search space.
Cite as
Sayan Bandyapadhyay and Eli Mitchell. Approximation and Parameterized Algorithms for Covering with Disks of Two Types of Radii. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bandyapadhyay_et_al:LIPIcs.WADS.2025.7,
author = {Bandyapadhyay, Sayan and Mitchell, Eli},
title = {{Approximation and Parameterized Algorithms for Covering with Disks of Two Types of Radii}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {7:1--7:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.7},
URN = {urn:nbn:de:0030-drops-242386},
doi = {10.4230/LIPIcs.WADS.2025.7},
annote = {Keywords: Covering, Disks, Approximation, FPT}
}
Document
Tight Bounds on the Number of Closest Pairs in Vertical Slabs
Abstract
Let S be a set of n points in ℝ^d, where d ≥ 2 is a constant, and let H₁,H₂,…,H_{m+1} be a sequence of vertical hyperplanes that are sorted by their first coordinates, such that exactly n/m points of S are between any two successive hyperplanes. Let |A(S,m)| be the number of different closest pairs in the {(m+1) choose 2} vertical slabs that are bounded by H_i and H_j, over all 1 ≤ i < j ≤ m+1. We prove tight bounds for the largest possible value of |A(S,m)|, over all point sets of size n, and for all values of 1 ≤ m ≤ n.
As a result of these bounds, we obtain, for any constant ε > 0, a data structure of size O(n), such that for any vertical query slab Q, the closest pair in the set Q ∩ S can be reported in O(n^{1/2+ε}) time. Prior to this work, no linear space data structure with sublinear query time was known.
Cite as
Ahmad Biniaz, Prosenjit Bose, Chaeyoon Chung, Jean-Lou De Carufel, John Iacono, Anil Maheshwari, Saeed Odak, Michiel Smid, and Csaba D. Tóth. Tight Bounds on the Number of Closest Pairs in Vertical Slabs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{biniaz_et_al:LIPIcs.WADS.2025.8,
author = {Biniaz, Ahmad and Bose, Prosenjit and Chung, Chaeyoon and De Carufel, Jean-Lou and Iacono, John and Maheshwari, Anil and Odak, Saeed and Smid, Michiel and T\'{o}th, Csaba D.},
title = {{Tight Bounds on the Number of Closest Pairs in Vertical Slabs}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {8:1--8:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.8},
URN = {urn:nbn:de:0030-drops-242391},
doi = {10.4230/LIPIcs.WADS.2025.8},
annote = {Keywords: closest pair, vertical slab, data structure}
}
Document
Online Routing in Directed Yao₄^∞ Graphs
Abstract
The x⃑{Yao₄^∞} and x⃑{Yao₄} graphs are two families of directed geometric graphs whose vertices are points in the plane, and each vertex has up to four outgoing edges. Consider a horizontal and a vertical line through each vertex v, defining four quadrants around v. Then v has an outgoing edge to the closest vertex in each of its four quadrants. When the distance is measured using the Euclidean norm, the resulting graph is the x⃑{Yao₄} graph, whereas with the L_∞-norm, we obtain the x⃑{Yao^{∞}₄} graph, which is a sub-graph of the well-known L_∞-Delaunay graph.
In this paper, we provide a local routing algorithm with routing ratio at most 85.22 for x⃑{Yao^{∞}₄} graphs. Prior to this work, no constant spanning or routing ratios for x⃑{Yao₄^∞} graphs were previously known. Now, x⃑{Yao₄^∞} graphs are the sparsest family of directed planar graphs supporting a competitive local routing strategy. Furthermore, we show that no local routing algorithm for x⃑{Yao₄^∞} graphs can have a routing ratio lower than 7+√2≈ 8.41. Moreover, we prove that the spanning ratio is at least 5+√2≈ 6.41 in the worst case. The techniques we develop in this paper also allow us to prove lower bounds of 7-√3+√{5-2√3}≈ 6.51 and 7+√2 for the spanning and routing ratios of x⃑{Yao₄}, respectively.
Cite as
Prosenjit Bose, Jean-Lou De Carufel, and John Stuart. Online Routing in Directed Yao₄^∞ Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 9:1-9:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bose_et_al:LIPIcs.WADS.2025.9,
author = {Bose, Prosenjit and De Carufel, Jean-Lou and Stuart, John},
title = {{Online Routing in Directed Yao₄^∞ Graphs}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {9:1--9:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.9},
URN = {urn:nbn:de:0030-drops-242404},
doi = {10.4230/LIPIcs.WADS.2025.9},
annote = {Keywords: Geometric Spanners, Yao Graphs, Local Routing Algorithms}
}
Document
On Geodesic Disks Enclosing Many Points
Abstract
Let Π(n) be the largest number such that for every set S of n points in a polygon P, there always exist two points x, y ∈ S, where every geodesic disk containing x and y contains Π(n) points of S. We establish upper and lower bounds for Π(n), and show that ⌈n/5⌉ +1 ≤ Π(n) ≤ ⌈n/4⌉ +1. We also show that there always exist two points x, y ∈ S such that every geodesic disk with x and y on its boundary contains at least 16/665(n-2) ≈ ⌈(n-2)/41.6⌉ points both inside and outside the disk. For the special case where the points of S are restricted to be the vertices of a geodesically convex polygon we give a tight bound of ⌈n/3⌉ + 1. We provide the same tight bound when we only consider geodesic disks having x and y as diametral endpoints. Finally, we give a lower bound of ⌈(n-2)/36⌉+2 for the two-colored version of the problem.
Cite as
Prosenjit Bose, Guillermo Esteban, David Orden, Rodrigo I. Silveira, and Tyler Tuttle. On Geodesic Disks Enclosing Many Points. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bose_et_al:LIPIcs.WADS.2025.10,
author = {Bose, Prosenjit and Esteban, Guillermo and Orden, David and Silveira, Rodrigo I. and Tuttle, Tyler},
title = {{On Geodesic Disks Enclosing Many Points}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {10:1--10:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.10},
URN = {urn:nbn:de:0030-drops-242414},
doi = {10.4230/LIPIcs.WADS.2025.10},
annote = {Keywords: Enclosing disks, Geodesic disks, Bichromatic}
}
Document
Crossing and Independent Families Among Polygons
Abstract
Given a set A of points in the plane, a family of line segments forming a matching in A is called crossing (or independent) if each pair of segments in the family intersects (or is non-intersecting, respectively). In past works, these notions have been generalized to polygons by identifying the points in A with the vertices of a given set of polygons and forbidding the line segments from intersecting or overlapping with polygon walls. In this work, we study the computational complexity of computing maximum crossing and independent families in this more general setting.
As our first two results, we show that both problems are NP-hard already when the polygons are triangles. Motivated by this, we turn to parameterized algorithms. For our main algorithmic results, we consider the number of polygons on the input as the natural parameter and under this parameterization obtain a fixed-parameter algorithm for computing a largest crossing family among these polygons, and a separate XP-algorithm for computing a largest independent family that lies in one of the faces of the polygonal domain.
Cite as
Anna Brötzner, Robert Ganian, Thekla Hamm, Fabian Klute, and Irene Parada. Crossing and Independent Families Among Polygons. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{brotzner_et_al:LIPIcs.WADS.2025.11,
author = {Br\"{o}tzner, Anna and Ganian, Robert and Hamm, Thekla and Klute, Fabian and Parada, Irene},
title = {{Crossing and Independent Families Among Polygons}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {11:1--11:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.11},
URN = {urn:nbn:de:0030-drops-242424},
doi = {10.4230/LIPIcs.WADS.2025.11},
annote = {Keywords: crossing families, crossing-free matchings, segment intersection graphs, computational geometry, parameterized algorithms}
}
Document
Testing Whether a Subgraph Is Convex or Isometric
Abstract
We consider the following two algorithmic problems: given a graph G and a subgraph H ⊆ G, decide whether H is an isometric or a geodesically convex subgraph of G. It is relatively easy to see that the problems can be solved by computing the distances between all pairs of vertices. We provide a conditional lower bound showing that, for sparse graphs with n vertices and Θ(n) edges, we cannot expect to solve the problem in O(n^{2-ε}) time for any constant ε > 0. We also show that the problem can be solved in subquadratic time for planar graphs and in near-linear time for graphs of bounded treewidth. Finally, we provide a near-linear time algorithm for the setting where G is a plane graph and H is defined by a few cycles in G.
Cite as
Sergio Cabello. Testing Whether a Subgraph Is Convex or Isometric. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{cabello:LIPIcs.WADS.2025.12,
author = {Cabello, Sergio},
title = {{Testing Whether a Subgraph Is Convex or Isometric}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {12:1--12:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.12},
URN = {urn:nbn:de:0030-drops-242439},
doi = {10.4230/LIPIcs.WADS.2025.12},
annote = {Keywords: convex subgraph, isometric subgraph, plane graph}
}
Document
Algorithms for Distance Problems in Continuous Graphs
Abstract
We study the problem of computing the diameter and the mean distance of a continuous graph, i.e., a connected graph where all points along the edges, instead of only the vertices, must be taken into account. It is known that for continuous graphs with m edges these values can be computed in roughly O(m²) time. In this paper, we use geometric techniques to obtain subquadratic time algorithms to compute the diameter and the mean distance of a continuous graph for two well-established classes of sparse graphs. We show that the diameter and the mean distance of a continuous graph of treewidth at most k can be computed in O(n log^O(k) n) time, where n is the number of vertices in the graph. We also show that computing the diameter and mean distance of a continuous planar graph with n vertices and F faces takes O(n F log n) time.
Cite as
Sergio Cabello, Delia Garijo, Antonia Kalb, Fabian Klute, Irene Parada, and Rodrigo I. Silveira. Algorithms for Distance Problems in Continuous Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{cabello_et_al:LIPIcs.WADS.2025.13,
author = {Cabello, Sergio and Garijo, Delia and Kalb, Antonia and Klute, Fabian and Parada, Irene and Silveira, Rodrigo I.},
title = {{Algorithms for Distance Problems in Continuous Graphs}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {13:1--13:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.13},
URN = {urn:nbn:de:0030-drops-242446},
doi = {10.4230/LIPIcs.WADS.2025.13},
annote = {Keywords: diameter, mean distance, continuous graph, treewidth, planar graph}
}
Document
Quantum Speedups for Polynomial-Time Dynamic Programming Algorithms
Abstract
We introduce a quantum dynamic programming framework that allows us to directly extend to the quantum realm a large body of classical dynamic programming algorithms. The corresponding quantum dynamic programming algorithms retain the same space complexity as their classical counterpart, while achieving a computational speedup. For a combinatorial (search or optimization) problem P and an instance I of P, such a speedup can be expressed in terms of the average degree δ of the {dependency digraph} G_𝒫(I) of I, determined by a recursive formulation of P. The nodes of this graph are the subproblems of P induced by I and its arcs are directed from each subproblem to those on whose solution it relies. In particular, our framework allows us to solve the considered problems in Õ(|V(G_𝒫(I))| √δ) time. As an example, we obtain a quantum version of the Bellman-Ford algorithm for computing shortest paths from a single source vertex to all the other vertices in a weighted n-vertex digraph with m edges that runs in Õ(n√{nm}) time, which improves the best known classical upper bound when m ∈ Ω(n^{1.4}).
Cite as
Susanna Caroppo, Giordano Da Lozzo, Giuseppe Di Battista, Michael T. Goodrich, and Martin Nöllenburg. Quantum Speedups for Polynomial-Time Dynamic Programming Algorithms. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 14:1-14:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{caroppo_et_al:LIPIcs.WADS.2025.14,
author = {Caroppo, Susanna and Da Lozzo, Giordano and Di Battista, Giuseppe and Goodrich, Michael T. and N\"{o}llenburg, Martin},
title = {{Quantum Speedups for Polynomial-Time Dynamic Programming Algorithms}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {14:1--14:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.14},
URN = {urn:nbn:de:0030-drops-242454},
doi = {10.4230/LIPIcs.WADS.2025.14},
annote = {Keywords: Dynamic Programming, Quantum Algorithms, Quantum Random Access Memory}
}
Document
Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs
Abstract
Enumerating minimal dominating sets with polynomial delay in bipartite graphs is a long-standing open problem. To date, even the subcase of chordal bipartite graphs is open, with the best known algorithm due to Golovach, Heggernes, Kanté, Kratsch, Sæther, and Villanger running in incremental-polynomial time. We improve on this result by providing a polynomial delay and space algorithm enumerating minimal dominating sets in chordal bipartite graphs. Additionally, we show that the total and connected variants admit polynomial and incremental-polynomial delay algorithms, respectively, within the same class. This provides an alternative proof of a result by Golovach et al. for total dominating sets, and answers an open question for the connected variant. Finally, we give evidence that the techniques used in this paper cannot be generalized to bipartite graphs for (total) minimal dominating sets, unless P = NP, and show that enumerating minimal connected dominating sets in bipartite graphs is harder than enumerating minimal transversals in general hypergraphs.
Cite as
Emanuel Castelo, Oscar Defrain, and Guilherme C. M. Gomes. Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{castelo_et_al:LIPIcs.WADS.2025.15,
author = {Castelo, Emanuel and Defrain, Oscar and C. M. Gomes, Guilherme},
title = {{Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {15:1--15:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.15},
URN = {urn:nbn:de:0030-drops-242467},
doi = {10.4230/LIPIcs.WADS.2025.15},
annote = {Keywords: algorithmic enumeration, minimal dominating sets, connected dominating sets, total dominating sets, chordal bipartite graphs, sequential method, polynomial delay}
}
Document
An Improved Guillotine Cut for Squares
Abstract
Given a set of n non-overlapping geometric objects, can we separate a constant fraction of them using straight-line cuts that extend from edge to edge? In 1996, Urrutia posed this question for compact convex objects. Pach and Tardos later refuted it for general line segments by constructing a family where any separable subfamily has size at most O (n^{log₃ 2}). However, for axis-parallel rectangles, they provided positive evidence, showing that an Ω(1/log n)-fraction can be separated.
This problem naturally arises in geometric approximation algorithms. In particular, when restricting cuts to only orthogonal straight lines, known as a guillotine cut sequence, any bound on the separability ratio directly translates into a clean and simple dynamic programming for computing a maximum independent set of geometric objects.
This paper focuses on the case when the objects are squares. For squares of arbitrary sizes, an Ω(1)-fraction can be separated (Abed et al., APPROX 2015), recently improved to 1/40 (and 1/160 ≈ 0.62% for the weighted case) (Khan and Pittu, APPROX 2020). We further improve this bound, showing that a 9/256 ≈ 3.51% can be separated for the weighted case. This result significantly narrows the possible range for squares to [3.51%, 50%]. The key to our improvement is a refined analysis of the existing framework.
Cite as
Parinya Chalermsook, Axel Kugelmann, Ly Orgo, Sumedha Uniyal, and Minoo Zarsav. An Improved Guillotine Cut for Squares. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{chalermsook_et_al:LIPIcs.WADS.2025.16,
author = {Chalermsook, Parinya and Kugelmann, Axel and Orgo, Ly and Uniyal, Sumedha and Zarsav, Minoo},
title = {{An Improved Guillotine Cut for Squares}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {16:1--16:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.16},
URN = {urn:nbn:de:0030-drops-242472},
doi = {10.4230/LIPIcs.WADS.2025.16},
annote = {Keywords: Guillotine cuts, Geometric Approximation Algorithms, Rectangles, Squares}
}
Document
Dynamic Streaming Algorithms for Geometric Independent Set
Abstract
We present the first space-efficient, fully dynamic streaming algorithm for computing a constant-factor approximation of the maximum independent set size of n axis-aligned rectangles in two dimensions. For an arbitrarily small constant δ > 0, our algorithm obtains an O((1/δ)²) approximation and requires O(U^δ polylog n) space and update time with high probability, assuming that coordinates are integers bounded by U. We also obtain a similar result for fat objects in any constant dimension. This extends recent non-streaming algorithms by Bhore and Chan from SODA'25, and also greatly extends previous streaming results, which were limited to special types of geometric objects such as one-dimensional intervals and unit disks.
Cite as
Timothy M. Chan and Yuancheng Yu. Dynamic Streaming Algorithms for Geometric Independent Set. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{chan_et_al:LIPIcs.WADS.2025.17,
author = {Chan, Timothy M. and Yu, Yuancheng},
title = {{Dynamic Streaming Algorithms for Geometric Independent Set}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {17:1--17:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.17},
URN = {urn:nbn:de:0030-drops-242481},
doi = {10.4230/LIPIcs.WADS.2025.17},
annote = {Keywords: Geometric Independent Set, Dynamic Streaming Algorithms}
}
Document
Parameterized Streaming Algorithms for Topological Sorting
Abstract
Computing a topological ordering for an n-node directed acyclic graph (DAG) G is computationally challenging in streaming models. Chakrabarti et al. {[}SODA 2020{]} showed that in the insertion-only streaming model, every single-pass algorithm requires Ω(n²) space, and every k-pass algorithm requires n^{1+Ω(1/k)} space for any constant k ≥ 1.
We study the parameterized complexity of streaming algorithms for topological sorting, considering two parameters: the independence number α and the maximum displacement δ. Our results include an O(1/ε)-pass O(α n^{1+ε})-space streaming algorithm and an O(n^{1/2})-pass O(n+δ²)-space streaming algorithm. For dense random DAGs, both α and δ are small, allowing us to improve the state-of-the-art for topological sorting in random DAGs.
As applications, we show that strongly connected components (SCC) decomposition and 2-satisfiability (2-SAT) can be solved in O(1/ε) passes using O(α n^{1+ε}) space and O(α_I n^{1+ε}) space, respectively, where α_I denotes the independence number of the implication graph induced by the input 2-SAT instance.
Cite as
Ho-Lin Chen, Peng-Ting Lin, and Meng-Tsung Tsai. Parameterized Streaming Algorithms for Topological Sorting. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{chen_et_al:LIPIcs.WADS.2025.18,
author = {Chen, Ho-Lin and Lin, Peng-Ting and Tsai, Meng-Tsung},
title = {{Parameterized Streaming Algorithms for Topological Sorting}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {18:1--18:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.18},
URN = {urn:nbn:de:0030-drops-242495},
doi = {10.4230/LIPIcs.WADS.2025.18},
annote = {Keywords: Independence Number, Chain Cover, SCC Decomposition, 2-Satisfiability}
}
Document
On the Enumeration of Signatures of XOR-CNF’s
Abstract
Given a CNF formula φ with clauses C_1, … , C_m over a set of variables V, a truth assignment 𝐚: V → {0, 1} generates a binary sequence σ_φ(𝐚) = (C_1(𝐚), …, C_m(𝐚)), called a signature of φ, where C_i(𝐚) = 1 if clause C_i evaluates to 1 under assignment 𝐚, and C_i(𝐚) = 0 otherwise. Signatures and their associated generation problems have given rise to new yet promising research questions in algorithmic enumeration. In a recent paper, Bérczi et al. interestingly proved that generating signatures of a CNF is tractable despite the fact that verifying a solution is hard. They also showed the hardness of finding maximal signatures of an arbitrary CNF due to the intractability of satisfiability in general. Their contribution leaves open the problem of efficiently generating maximal signatures for tractable classes of CNFs, i.e., those for which satisfiability can be solved in polynomial time. Stepping into that direction, we completely characterize the complexity of generating all, minimal, and maximal signatures for XOR-CNF’s.
Cite as
Nadia Creignou, Oscar Defrain, Frédéric Olive, and Simon Vilmin. On the Enumeration of Signatures of XOR-CNF’s. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{creignou_et_al:LIPIcs.WADS.2025.19,
author = {Creignou, Nadia and Defrain, Oscar and Olive, Fr\'{e}d\'{e}ric and Vilmin, Simon},
title = {{On the Enumeration of Signatures of XOR-CNF’s}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {19:1--19:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.19},
URN = {urn:nbn:de:0030-drops-242508},
doi = {10.4230/LIPIcs.WADS.2025.19},
annote = {Keywords: Algorithmic enumeration, XOR-CNF, signatures, maximal bipartite subgraphs enumeration, extension, proximity search}
}
Document
Routing Few Robots in a Crowded Network
Abstract
In Graph Coordinated Motion Planning, we are given a graph G some of whose vertices are occupied by robots, and we are asked to route k marked robots to their destinations while avoiding collisions and without exceeding a given budget 𝓁 on the number of robot moves. We continue the recent investigation of the problem [ICALP 2024], focusing on the parameter k that captures the task of routing a small number of robots in a possibly crowded graph. We prove that the problem is W[1]-hard parameterized by 𝓁 even for k = 1, but fixed-parameter tractable parameterized by k plus the treedepth of G. We complement the latter algorithm with an NP-hardness reduction which shows that both parameters are necessary to achieve tractability.
Cite as
Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, Dominik Leko, and M. S. Ramanujan. Routing Few Robots in a Crowded Network. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{deligkas_et_al:LIPIcs.WADS.2025.20,
author = {Deligkas, Argyrios and Eiben, Eduard and Ganian, Robert and Kanj, Iyad and Leko, Dominik and Ramanujan, M. S.},
title = {{Routing Few Robots in a Crowded Network}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {20:1--20:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.20},
URN = {urn:nbn:de:0030-drops-242516},
doi = {10.4230/LIPIcs.WADS.2025.20},
annote = {Keywords: graph coordinated motion planning, parameterized complexity, treedepth}
}
Document
A WSPD, Separator and Small Tree Cover for c-Packed Graphs
Abstract
The c-packedness property, proposed in 2010, is a geometric property that captures the spatial distribution of a set of edges. Despite the recent interest in c-packedness, its utility has so far been limited to Fréchet distance problems. An open problem is whether a wider variety of algorithmic and data structure problems can be solved efficiently under the c-packedness assumption, and more specifically, on c-packed graphs.
In this paper, we prove two fundamental properties of c-packed graphs: that there exists a linear-size well-separated pair decomposition under the graph metric, and there exists a constant size balanced separator. We then apply these fundamental properties to obtain a small tree cover for the metric space and distance oracles under the shortest path metric. In particular, we obtain a tree cover of constant size, an exact distance oracle of near-linear size and an approximate distance oracle of linear size.
Cite as
Lindsey Deryckere, Joachim Gudmundsson, André van Renssen, Yuan Sha, and Sampson Wong. A WSPD, Separator and Small Tree Cover for c-Packed Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{deryckere_et_al:LIPIcs.WADS.2025.21,
author = {Deryckere, Lindsey and Gudmundsson, Joachim and van Renssen, Andr\'{e} and Sha, Yuan and Wong, Sampson},
title = {{A WSPD, Separator and Small Tree Cover for c-Packed Graphs}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {21:1--21:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.21},
URN = {urn:nbn:de:0030-drops-242529},
doi = {10.4230/LIPIcs.WADS.2025.21},
annote = {Keywords: Well-separated pair decomposition, separator, tree cover, distance oracles, realistic graphs}
}
Document
On Minimizing Wiggle in Stacked Area Charts
Abstract
Stacked area charts are a widely used visualization technique for numerical time series. The x-axis represents time, and the time series are displayed as horizontal, variable-height layers stacked on top of each other. The height of each layer corresponds to the time series values at each time point. The main aesthetic criterion for optimizing the readability of stacked area charts is the amount of vertical change of the borders between the time series in the visualization, called wiggle. While many heuristic algorithms have been developed to minimize wiggle, the computational complexity of minimizing wiggle has not been formally analyzed. In this paper, we show that different variants of wiggle minimization are NP-hard and even hard to approximate. We also present an exact mixed-integer linear programming formulation and compare its performance with a state-of-the-art heuristic in an experimental evaluation. Lastly, we consider a special case of wiggle minimization that corresponds to the fundamentally interesting and natural problem of ordering a set of numbers as to minimize their sum of absolute prefix sums. We show several complexity results for this problem that imply some of the mentioned hardness results for wiggle minimization.
Cite as
Alexander Dobler and Martin Nöllenburg. On Minimizing Wiggle in Stacked Area Charts. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{dobler_et_al:LIPIcs.WADS.2025.22,
author = {Dobler, Alexander and N\"{o}llenburg, Martin},
title = {{On Minimizing Wiggle in Stacked Area Charts}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {22:1--22:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.22},
URN = {urn:nbn:de:0030-drops-242530},
doi = {10.4230/LIPIcs.WADS.2025.22},
annote = {Keywords: Stacked area charts, NP-hardness, Mixed-integer linear programming}
}
Document
Novel Complexity Results for Temporal Separators with Deadlines
Abstract
We consider two variants, (s,z,𝓁)-Temporal Separator and (s,z,𝓁)-Temporal Cut, respectively, of the vertex separator and the edge cut problem in temporal graphs. The goal is to remove the minimum number of vertices (temporal edges, respectively) in order to delete all the temporal paths that have time travel at most 𝓁 between a source vertex s and target vertex z. First, we solve an open problem in the literature showing that (s,z,𝓁)-Temporal Separator is NP-hard even when the underlying graph has pathwidth bounded by four. We complement this result showing that (s,z,𝓁)-Temporal Separator can be solved in polynomial time for graphs of pathwidth bounded by three. Then we consider the approximability of (s,z,𝓁)-Temporal Separator and we show that it cannot be approximated within factor 2^Ω(log^{1-ε}|V|) for any constant ε > 0, unless NP ⊆ ZPP (V is the vertex set of the input temporal graph) and that the strict version is approximable within factor 𝓁-1 (we show also that it is unliklely that this factor can be improved). Then we consider the (s,z,𝓁)-Temporal Cut problem, we show that it is APX-hard and we present a 2 log₂(2𝓁) approximation algorithm.
Cite as
Riccardo Dondi and Manuel Lafond. Novel Complexity Results for Temporal Separators with Deadlines. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{dondi_et_al:LIPIcs.WADS.2025.23,
author = {Dondi, Riccardo and Lafond, Manuel},
title = {{Novel Complexity Results for Temporal Separators with Deadlines}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {23:1--23:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.23},
URN = {urn:nbn:de:0030-drops-242545},
doi = {10.4230/LIPIcs.WADS.2025.23},
annote = {Keywords: Temporal Graphs, Graph Algorithms, Graph Separators, Parameterized Complexity, Approximation Complexity}
}
Document
Computational Geometry with Probabilistically Noisy Primitive Operations
Abstract
Much prior work has been done on designing computational geometry algorithms that handle input degeneracies, data imprecision, and arithmetic round-off errors. We take a new approach, inspired by the noisy sorting literature, and study computational geometry algorithms subject to noisy Boolean primitive operations in which, e.g., the comparison "is point q above line 𝓁?" returns the wrong answer with some fixed probability. We propose a novel technique called path-guided pushdown random walks that generalizes the results of noisy sorting. We apply this technique to solve point-location, plane-sweep, convex hulls in 2D and 3D, and Delaunay triangulations for noisy primitives in optimal time with high probability.
Cite as
David Eppstein, Michael T. Goodrich, and Vinesh Sridhar. Computational Geometry with Probabilistically Noisy Primitive Operations. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{eppstein_et_al:LIPIcs.WADS.2025.24,
author = {Eppstein, David and Goodrich, Michael T. and Sridhar, Vinesh},
title = {{Computational Geometry with Probabilistically Noisy Primitive Operations}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {24:1--24:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.24},
URN = {urn:nbn:de:0030-drops-242552},
doi = {10.4230/LIPIcs.WADS.2025.24},
annote = {Keywords: Computational geometry, noisy comparisons, random walks}
}
Document
An Efficient Polynomial Time Approximation Scheme for Minimizing the Total Weighted Completion Time on Uniformly Related Machines
Abstract
We study a classic scheduling problem on uniformly related machines for which we show an efficient polynomial time approximation scheme (EPTAS), where an EPTAS is a fast and practical approximation scheme. For a desired approximation ratio of 1+ε for ε > 0, the running time of an EPTAS is a function of ε multiplied by a polynomial function of the input length. New methods and techniques are essential in developing such improved approximation schemes, and their design is a primary goal of this research agenda. We present an EPTAS for the scheduling problem of a set of jobs on uniformly related machines so as to minimize the total weighted completion time. The problem is NP-hard in the strong sense, and therefore an EPTAS is the best possible approximation scheme for the problem, unless P=NP. Prior to our work, only a PTAS was known for the problem, while an EPTAS was known only for the special case of identical machines.
Cite as
Leah Epstein and Asaf Levin. An Efficient Polynomial Time Approximation Scheme for Minimizing the Total Weighted Completion Time on Uniformly Related Machines. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 25:1-25:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{epstein_et_al:LIPIcs.WADS.2025.25,
author = {Epstein, Leah and Levin, Asaf},
title = {{An Efficient Polynomial Time Approximation Scheme for Minimizing the Total Weighted Completion Time on Uniformly Related Machines}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {25:1--25:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.25},
URN = {urn:nbn:de:0030-drops-242564},
doi = {10.4230/LIPIcs.WADS.2025.25},
annote = {Keywords: Scheduling algorithms, Approximation schemes, Min-sum objective}
}
Document
Lower Bounds for Several Standard Bin Packing Algorithms in the Random Order Model
Abstract
We consider the performance of standard bin packing algorithms in the random order model. We provide an improved lower bound of 1.15582656 on the asymptotic approximation ratio of Best Fit (BF) for randomly ordered inputs. We also show lower bounds on the asymptotic approximation ratio for two bounded space bin packing algorithms in this model, namely for 2-BF and 2-FF. These are well-studied bounded space algorithms and the first one has the same asymptotic worst-case performance as BF. However, the resulting lower bounds on their performances in the random order model are much higher than that of BF.
Cite as
Leah Epstein and Asaf Levin. Lower Bounds for Several Standard Bin Packing Algorithms in the Random Order Model. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{epstein_et_al:LIPIcs.WADS.2025.26,
author = {Epstein, Leah and Levin, Asaf},
title = {{Lower Bounds for Several Standard Bin Packing Algorithms in the Random Order Model}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {26:1--26:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.26},
URN = {urn:nbn:de:0030-drops-242577},
doi = {10.4230/LIPIcs.WADS.2025.26},
annote = {Keywords: Bin packing, Best Fit, Random order, Bounded space algorithms}
}
Document
A QPTAS for Facility Location on Unit Disk Graphs
Abstract
We study the classic (Uncapacitated) Facility Location problem on Unit Disk Graphs (UDGs). For a given point set P in the plane, the unit disk graph UDG(P) on P has vertex set P and an edge between two distinct points p, q ∈ P if and only if their Euclidean distance |pq| is at most 1. The weight of the edge pq is equal to their distance |pq|. An instance of {Facility Location} on UDG(P) consists of a set C ⊆ P of clients and a set F ⊆ P of facilities, each having an opening cost f_i. The goal is to pick a subset F' ⊆ F to open while minimizing ∑_{i ∈ F'} f_i + ∑_{v ∈ C} d(v,F'), where d(v,F') is the distance of v to nearest facility in F' through UDG(P).
In this paper, we present the first Quasi-Polynomial Time Approximation Schemes (QPTAS) for the problem. While approximation schemes are well-established for facility location problems on sparse geometric graphs (such as planar graphs), there is a lack of such results for dense graphs. Specifically, prior to this study, to the best of our knowledge, there was no approximation scheme for any facility location problem on UDGs in the general setting.
Cite as
Zachary Friggstad, Mohsen Rezapour, Mohammad R. Salavatipour, and Hao Sun. A QPTAS for Facility Location on Unit Disk Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{friggstad_et_al:LIPIcs.WADS.2025.27,
author = {Friggstad, Zachary and Rezapour, Mohsen and Salavatipour, Mohammad R. and Sun, Hao},
title = {{A QPTAS for Facility Location on Unit Disk Graphs}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {27:1--27:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.27},
URN = {urn:nbn:de:0030-drops-242586},
doi = {10.4230/LIPIcs.WADS.2025.27},
annote = {Keywords: Facility Location, Unit Disk Graphs, Approximation Algorithms}
}
Document
Approximation Algorithms for the Generalized Point-To-Point Problem
Abstract
We consider the Generalized Point-to-Point (GP2P) problem in which we have an edge-weighted graph G with (possibly negative) node charges ϕ(v) ∈ ℤ. The goal is to find a minimum-cost set of edges such that each component has nonnegative total charge. Viewing the positive charges as specifying supply and negative charges as demand quantities at various nodes, the problem is equivalent to build the cheapest network so that it is possible to satisfy all demands by routing supplies across the network.
This problem is a significant generalization of other network design problems such as the well-studied Steiner Forest problem. Even the special case of only having one single demand point (having charge -k and all the other nodes having charge +1) is capturing the k-Minimum Spanning Tree problem. Earlier work by Hajiaghayi et al. (2016) [Hajiaghayi et al., 2016] gave an O(log n) approximation in pseudo-polynomial time with further improved guarantees if the total supply is not much larger than the total demand, and also a 2-approximation if the total supply equals the total demand.
Our contributions are four-fold: (a) we show how known k-Minimum Spanning Tree approximations can be extended to GP2P approximations while losing only a ε-factor if the number of demand points in the instance is bounded by a constant, (b) we improve the running time to be Fixed-Parameter Tractable (FPT) in the number of demand points in constant-dimensional Euclidean metrics, (c) we give a 2-approximation in instances where edge costs are all 1 and ϕ(v) = ± 1 for each node v and show such instances are APX-hard, and (d) we show how the logarithmic approximations in earlier work can be modified to run in truly polynomial time.
Cite as
Zachary Friggstad, Mohammad R. Salavatipour, and Hao Sun. Approximation Algorithms for the Generalized Point-To-Point Problem. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{friggstad_et_al:LIPIcs.WADS.2025.28,
author = {Friggstad, Zachary and Salavatipour, Mohammad R. and Sun, Hao},
title = {{Approximation Algorithms for the Generalized Point-To-Point Problem}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {28:1--28:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.28},
URN = {urn:nbn:de:0030-drops-242599},
doi = {10.4230/LIPIcs.WADS.2025.28},
annote = {Keywords: Point-to-Point Network design, Approximation, Steiner Forest, k-MST}
}
Document
Linear Layouts of Graphs with Priority Queues
Abstract
A linear layout of a graph consists of a linear ordering of its vertices and a partition of its edges into pages such that the edges assigned to the same page obey some constraint. The two most prominent and widely studied types of linear layouts are stack and queue layouts, in which any two edges assigned to the same page are forbidden to cross and nest, respectively. The names of these two layouts derive from the fact that, when parsing the graph according to the linear vertex ordering, the edges in a single page can be stored using a single stack or queue, respectively. Recently, the concepts of stack and queue layouts have been extended by using a double-ended queue or a restricted-input queue for storing the edges of a page. We extend this line of study to edge-weighted graphs by introducing priority queue layouts, that is, the edges on each page are stored in a priority queue whose keys are the edge weights. First, we show that there are edge-weighted graphs that require a linear number of priority queues. Second, we characterize the graphs that admit a priority queue layout with a single queue, regardless of the edge-weight function, and we provide an efficient recognition algorithm. Third, we show that the number of priority queues required independently of the edge-weight function is bounded by the pathwidth of the graph, but can be arbitrarily large already for graphs of treewidth two. Finally, we prove that determining the minimum number of priority queues is NP-complete if the linear ordering of the vertices is fixed.
Cite as
Emilio Di Giacomo, Walter Didimo, Henry Förster, Torsten Ueckerdt, and Johannes Zink. Linear Layouts of Graphs with Priority Queues. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{digiacomo_et_al:LIPIcs.WADS.2025.29,
author = {Di Giacomo, Emilio and Didimo, Walter and F\"{o}rster, Henry and Ueckerdt, Torsten and Zink, Johannes},
title = {{Linear Layouts of Graphs with Priority Queues}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {29:1--29:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.29},
URN = {urn:nbn:de:0030-drops-242602},
doi = {10.4230/LIPIcs.WADS.2025.29},
annote = {Keywords: linear layouts, recognition and characterization, priority queue layouts}
}
Document
Convolution and Knapsack in Higher Dimensions
Abstract
In the Knapsack problem, one is given the task of packing a knapsack of a given size with items in order to gain a packing with a high profit value. As one of the most classical problems in computer science, research for this problem has gone a long way. One important connection to the (max,+)-convolution problem has been established, where knapsack solutions can be combined by building the convolution of two sequences. This observation has been used in recent years to give conditional lower bounds but also parameterized algorithms.
In this paper we carry these results into higher dimensions. We consider Knapsack where items are characterized by multiple properties - given through a vector - and a knapsack that has a capacity vector. The packing must not exceed any of the given capacity constraints. In order to show a similar sub-quadratic lower bound we consider a multidimensional version of (max, +)-convolution. We then consider variants of this problem introduced by Cygan et al. and prove that they are all equivalent in terms of algorithms that allow for a running time sub-quadratic in the number of entries of the array.
We further develop a parameterized algorithm to solve higher dimensional Knapsack. The techniques we apply are inspired by an algorithm introduced by Axiotis and Tzamos. We will show that even for higher dimensional Knapsack, we can reduce the problem to convolution on one-dimensional, concave sequences, leading to an 𝒪(dn + dD ⋅ max{(Π_{i=1}^d t_i), t_max log t_max}) algorithm, where D is the number of different weight vectors, t the capacity vector and d is the dimension of the problem. Then, we use the techniques to improve the approach of Eisenbrand and Weismantel to obtain an algorithm for Integer Linear Programming with upper bounds with running time 𝒪(dn) + D ⋅ 𝒪(d Δ)^{d(d+1)} + T_LP.
Finally, we give an divide-and-conquer algorithm for ILP with running time n^{d+1} ⋅ O(Δ)^d ⋅ log(|u - 𝓁|_∞).
Cite as
Kilian Grage, Klaus Jansen, and Björn Schumacher. Convolution and Knapsack in Higher Dimensions. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{grage_et_al:LIPIcs.WADS.2025.30,
author = {Grage, Kilian and Jansen, Klaus and Schumacher, Bj\"{o}rn},
title = {{Convolution and Knapsack in Higher Dimensions}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {30:1--30:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.30},
URN = {urn:nbn:de:0030-drops-242618},
doi = {10.4230/LIPIcs.WADS.2025.30},
annote = {Keywords: Knapsack, Convolution, Integer Linear Programming}
}
Document
Repairing Schedules by Removing Waiting Times: A Parameterized Complexity Analysis
Abstract
We consider the problem of repairing production schedules in a job-shop setting by reducing pre-planned waiting times. Herein, a schedule of all jobs is given. To compensate unforeseen disturbances, this schedule contains waiting times between the execution of two consecutive tasks of a job. Further, we assume that the schedule temporarily overloads some machines, e.g. due to reduced machine capacities because of worker sickness or (partially) broken machines. We study the problem of removing as few waiting times as possible in order to eliminate the machine overloads. After formalizing this problem, we perform an extensive analysis of its parameterized complexity with respect to several natural parameters, resulting in a detailed picture of the problem’s complexity.
Cite as
Niels Grüttemeier and Klaus Heeger. Repairing Schedules by Removing Waiting Times: A Parameterized Complexity Analysis. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{gruttemeier_et_al:LIPIcs.WADS.2025.31,
author = {Gr\"{u}ttemeier, Niels and Heeger, Klaus},
title = {{Repairing Schedules by Removing Waiting Times: A Parameterized Complexity Analysis}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {31:1--31:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.31},
URN = {urn:nbn:de:0030-drops-242624},
doi = {10.4230/LIPIcs.WADS.2025.31},
annote = {Keywords: Job shop, parallel machines, reactive scheduling}
}
Document
Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems
Abstract
Parameterized local search combines classic local search heuristics with the paradigm of parameterized algorithmics. While most local search algorithms aim to improve given solutions by performing one single operation on a given solution, the parameterized approach aims to improve a solution by performing k simultaneous operations. Herein, k is a parameter called search radius for which the value can be chosen by a user. One major goal in the field of parameterized local search is to outline the trade-off between the size of k and the running time of the local search step.
In this work, we introduce an abstract framework that generalizes natural parameterized local search approaches for a large class of partitioning problems: Given n items that are partitioned into b bins and a target function that evaluates the quality of the current partition, one asks whether it is possible to improve the solution by removing up to k items from their current bins and reassigning them to other bins. Among others, our framework applies for the local search versions of problems like Cluster Editing, Vector Bin Packing, and Nash Social Welfare. Motivated by a real-world application of the problem Vector Bin Packing, we introduce a parameter called number of types τ ≤ n and show that all problems fitting in our framework can be solved in τ^k ⋅ 2^𝒪(k) ⋅ |I|^𝒪(1) time, where |I| denotes the total input size. In case of Cluster Editing, the parameter τ generalizes the well-known parameter neighborhood diversity of the input graph.
We complement these algorithms by showing that for all considered problems, an algorithm significantly improving over our algorithm with running time τ^k ⋅ 2^𝒪(k) ⋅ |I|^𝒪(1) would contradict the Exponential Time Hypothesis. Additionally, we show that even on very restricted instances, all considered problems are W[1]-hard when parameterized by the search radius k alone. In case of the local search version of Vector Bin Packing, we provide an even stronger W[1]-hardness result.
Cite as
Niels Grüttemeier, Nils Morawietz, and Frank Sommer. Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{gruttemeier_et_al:LIPIcs.WADS.2025.32,
author = {Gr\"{u}ttemeier, Niels and Morawietz, Nils and Sommer, Frank},
title = {{Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {32:1--32:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.32},
URN = {urn:nbn:de:0030-drops-242631},
doi = {10.4230/LIPIcs.WADS.2025.32},
annote = {Keywords: Flip-Neighborhood, Cluster Editing, Vector Bin Packing, Vertex Cover, NP-hard problem, Max c-Cut}
}
Document
Spanner for the 0/1/∞ Weighted Region Problem
Abstract
We consider the problem of computing an approximate weighted shortest path in a weighted planar subdivision, with weights assigned from the set {0, 1, ∞}. The subdivision includes zero-cost regions (0-regions) with weight 0 and obstacles with weight ∞, all embedded in a plane with weight 1. In a polygonal domain, where the 0-regions and obstacles are non-overlapping polygons (not necessarily convex) with in total N vertices, we present an algorithm that computes a (1 + ε)-approximate spanner of the input vertices in expected Õ(N/ε³) time, for 0 < ε < 1. Using our spanner, we can compute a (1 + ε)-approximate weighted shortest path between any two points (not necessarily vertices) in Õ(N/ε³) time. Furthermore, we prove that our results more generally apply to non-polygonal convex regions. Using this generalisation, one can approximate the weak partial Fréchet similarity [Buchin et al., 2009] between two polygonal curves in expected Õ(n²/ε²) time, where n is the total number of vertices of the input curves.
Cite as
Joachim Gudmundsson, Zijin Huang, André van Renssen, and Sampson Wong. Spanner for the 0/1/∞ Weighted Region Problem. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 33:1-33:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{gudmundsson_et_al:LIPIcs.WADS.2025.33,
author = {Gudmundsson, Joachim and Huang, Zijin and van Renssen, Andr\'{e} and Wong, Sampson},
title = {{Spanner for the 0/1/∞ Weighted Region Problem}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {33:1--33:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.33},
URN = {urn:nbn:de:0030-drops-242644},
doi = {10.4230/LIPIcs.WADS.2025.33},
annote = {Keywords: weighted region problem, approximate shortest path, spanner}
}
Document
Link Diameter, Radius and 2-Point Link Distance Queries in Polygonal Domains
Abstract
We show how to preprocess a polygonal domain with holes so that the link distance (the number of links in a minimum-link path) between two query points in the domain can be reported efficiently. Using our data structures, the link diameter of the domain (i.e., the maximum number of links that may be required in a minimum-link path between two points in the domain) as well as the link center and radius of the domain (i.e., the point minimizing the maximum link distance to the furthest point in the domain and this maximum link distance) can be found in polynomial time. We also give a simpler algorithm for finding the link diameter, not using the link distance query structures. Answering 2-point link distance queries and computing the link diameter/radius/center in polygonal domains have been open questions since these problems were studied for simple polygons in the 90’s.
Cite as
Mart Hagedoorn and Valentin Polishchuk. Link Diameter, Radius and 2-Point Link Distance Queries in Polygonal Domains. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{hagedoorn_et_al:LIPIcs.WADS.2025.34,
author = {Hagedoorn, Mart and Polishchuk, Valentin},
title = {{Link Diameter, Radius and 2-Point Link Distance Queries in Polygonal Domains}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {34:1--34:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.34},
URN = {urn:nbn:de:0030-drops-242659},
doi = {10.4230/LIPIcs.WADS.2025.34},
annote = {Keywords: Minimum-link paths, link distance, diameter, center, radius, 2-point distance queries}
}
Document
Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage
Abstract
We improve the recent succinct data structure result of Balakrishnan et al. for chordal graphs with bounded vertex leafage (SWAT 2024). A chordal graph is a widely studied graph class which can be characterized as the intersection graph of subtrees of a host tree, denoted as a tree representation of the chordal graph. The vertex leafage and leafage parameters of a chordal graph deal with the existence of a tree representation with a bounded number of leaves in either the subtrees representing the vertices or the host tree itself.
We simplify the lower bound proof of Balakrishnan et al. which applied to only chordal graphs with bounded vertex leafage, and extend it to a lower bound proof for chordal graphs with bounded leafage as well. For both classes of graphs, the information-theoretic lower bound we (re-)obtain for k = o(n) is (k-1)nlog n - knlog k - o(knlog n) bits, where the leafage or vertex leafage of the graph is at most k = o(n). We further extend the range of the parameter k to Θ(n) as well.
Then we give a succinct data structure using (k-1)nlog (n/k) + o(knlog n) bits to answer adjacent queries, which test the adjacency between pairs of vertices, in O((log k)/(log log n) + 1) time compared to the O(klog n) time of the data structure of Balakrishnan et al. For the neighborhood query which lists the neighbours of a given vertex, our query time is O((log n)/(log log n)) per neighbour compared to O(k²log n) per neighbour.
We also extend the data structure ideas to obtain a succinct data structure for chordal graphs with bounded leafage k, answering an open question of Balakrishnan et al. Our succinct data structure, which uses (k-1)nlog (n/k) + o(knlog n) bits, has query time O(1) for the adjacent query and O(1) per neighbour for the neighborhood query. Using slightly more space (an additional (1+ε)nlog n bits for any ε > 0) allows distance queries, which compute the number of edges in the shortest path between two given vertices, to be answered in O(1) time as well.
Cite as
Meng He and Kaiyu Wu. Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 35:1-35:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{he_et_al:LIPIcs.WADS.2025.35,
author = {He, Meng and Wu, Kaiyu},
title = {{Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {35:1--35:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.35},
URN = {urn:nbn:de:0030-drops-242660},
doi = {10.4230/LIPIcs.WADS.2025.35},
annote = {Keywords: Chordal Graph, Leafage, Vertex Leafage, Succinct Data Structure}
}
Document
On the Complexity of Minimising the Moving Distance for Dispersing Objects
Abstract
We study Geometric Graph Edit Distance (GGED), a graph-editing model to compute the minimum edit distance of intersection graphs that uses moving objects as an edit operation. We first show an O(n log n)-time algorithm that minimises the total moving distance to disperse unit intervals. This algorithm is applied to render a given unit interval graph (i) edgeless, (ii) acyclic and (iii) k-clique-free. We next show that GGED becomes strongly NP-hard when rendering a weighted interval graph (i) edgeless, (ii) acyclic and (iii) k-clique-free. Lastly, we prove that minimising the maximum moving distance for rendering a unit disk graph edgeless is strongly NP-hard over the L₁ and L₂ distances.
Cite as
Nicolás Honorato-Droguett, Kazuhiro Kurita, Tesshu Hanaka, and Hirotaka Ono. On the Complexity of Minimising the Moving Distance for Dispersing Objects. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{honoratodroguett_et_al:LIPIcs.WADS.2025.36,
author = {Honorato-Droguett, Nicol\'{a}s and Kurita, Kazuhiro and Hanaka, Tesshu and Ono, Hirotaka},
title = {{On the Complexity of Minimising the Moving Distance for Dispersing Objects}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {36:1--36:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.36},
URN = {urn:nbn:de:0030-drops-242673},
doi = {10.4230/LIPIcs.WADS.2025.36},
annote = {Keywords: Intersection graphs, Optimisation, Graph modification}
}
Document
A Near-Linear Time Exact Algorithm for the L₁-Geodesic Fréchet Distance Between Two Curves on the Boundary of a Simple Polygon
Abstract
Let P be a polygon with k vertices. Let R and B be two simple, interior disjoint curves on the boundary of P, with n and m vertices. We show how to compute the Fréchet distance between R and B using the geodesic L₁-distance in P in 𝒪(k log nm + (n+m) (log² nm log k + log⁴ nm)) time.
Cite as
Thijs van der Horst, Marc van Kreveld, Tim Ophelders, and Bettina Speckmann. A Near-Linear Time Exact Algorithm for the L₁-Geodesic Fréchet Distance Between Two Curves on the Boundary of a Simple Polygon. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 37:1-37:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{vanderhorst_et_al:LIPIcs.WADS.2025.37,
author = {van der Horst, Thijs and van Kreveld, Marc and Ophelders, Tim and Speckmann, Bettina},
title = {{A Near-Linear Time Exact Algorithm for the L₁-Geodesic Fr\'{e}chet Distance Between Two Curves on the Boundary of a Simple Polygon}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {37:1--37:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.37},
URN = {urn:nbn:de:0030-drops-242681},
doi = {10.4230/LIPIcs.WADS.2025.37},
annote = {Keywords: Fr\'{e}chet distance, geodesic, simple polygon}
}
Document
Clustering Point Sets Revisited
Abstract
In the sets clustering problem one is given a collection of point sets 𝒫 = {P_1,… P_m} in ℝ^d, where for any set of k centers in ℝ^d, each P_i is assigned to its nearest center as determine by some local cost functions. The goal is then to select a set of k centers to minimize some global cost function of the corresponding local assignment costs. Specifically, we consider either summing or taking the maximum cost over all P_i, where for each P_i the cost of assigning it to a center c is either max_{p ∈ P_i} ‖c-p‖, ∑_{p ∈ P_i} ‖c-p‖, or ∑_{p ∈ P_i} ‖c-p‖².
Different combinations of the global and local cost functions naturally generalize the k-center, k-median, and k-means clustering problems. In this paper, we improve the prior results for the natural generalization of k-center, give the first result for the natural generalization of k-means, and give results for generalizations of k-median and k-center which differ from those previously studied.
Cite as
Md. Billal Hossain and Benjamin Raichel. Clustering Point Sets Revisited. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{hossain_et_al:LIPIcs.WADS.2025.38,
author = {Hossain, Md. Billal and Raichel, Benjamin},
title = {{Clustering Point Sets Revisited}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {38:1--38:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.38},
URN = {urn:nbn:de:0030-drops-242693},
doi = {10.4230/LIPIcs.WADS.2025.38},
annote = {Keywords: Clustering, k-center, k-median, k-means}
}
Document
Sweeping a Domain with Line-Of-Sight Between Covisible Agents
Abstract
We consider sweeping a polygonal domain using variable-length segments whose endpoints can be considered to be mobile agents moving with bounded speeds; a point in the domain is swept when it belongs to one of the segments. The objective is to sweep the domain as quickly as possible. We show that the problem is NP-hard even in simple polygons and even for a single segment (two agents), and give constant-factor approximation algorithms, both for simple polygons and polygons with holes.
Our approximations are obtained by introducing a new type of "window partition" of the polygon, which may find other applications. For domains with holes, our results are based on a non-trivial topological argument proving a surprising fact: a connected subset of the domain, whose points are swept but not directly touched by the agents, may contain at most one hole.
Cite as
Kien C. Huynh, Joseph S. B. Mitchell, and Valentin Polishchuk. Sweeping a Domain with Line-Of-Sight Between Covisible Agents. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 39:1-39:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{huynh_et_al:LIPIcs.WADS.2025.39,
author = {Huynh, Kien C. and Mitchell, Joseph S. B. and Polishchuk, Valentin},
title = {{Sweeping a Domain with Line-Of-Sight Between Covisible Agents}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {39:1--39:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.39},
URN = {urn:nbn:de:0030-drops-242706},
doi = {10.4230/LIPIcs.WADS.2025.39},
annote = {Keywords: Polygon sweeping, collaborating agents, motion coordination, makespan optimization}
}
Document
Grandchildren-Weight-Balanced Binary Search Trees
Abstract
We revisit weight-balanced trees, also known as trees of bounded balance. Invented by Nievergelt and Reingold in 1972, these trees are obtained by assigning a weight to each node and requesting that the weight of each node should be quite larger than the weights of its children, the precise meaning of "quite larger" depending on a real-valued parameter γ. Blum and Mehlhorn then showed how to maintain them in a recursive (bottom-up) fashion when 2/11 ⩽ γ ⩽ 1-1/√2, their algorithm requiring only an amortised constant number of tree rebalancing operations per update (insertion or deletion). Later, in 1993, Lai and Wood proposed a top-down procedure for updating these trees when 2/11 ⩽ γ ⩽ 1/4.
Our contribution is two-fold. First, we strengthen the requirements of Nievergelt and Reingold, by also requesting that each node should have a substantially larger weight than its grandchildren, thereby obtaining what we call grandchildren-balanced trees. Grandchildren-balanced trees are not harder to maintain than weight-balanced trees, but enjoy a smaller node depth, both in the worst case (with a 6 % decrease) and on average (with a 1.6 % decrease). In particular, unlike standard weight-balanced trees, all grandchildren-balanced trees with n nodes are of height less than 2 log₂(n).
Second, we adapt the algorithm of Lai and Wood to all weight-balanced trees, i.e., to all parameter values γ such that 2/11 ⩽ γ ⩽ 1-1/√2. More precisely, we adapt it to all grandchildren-balanced trees for which 1/4 < γ ⩽ 1 - 1/√2. Finally, we show that, except in limit cases (where, for instance, γ = 1 - 1/√2), all these algorithms result in making a constant amortised number of tree rebalancing operations per tree update.
Cite as
Vincent Jugé. Grandchildren-Weight-Balanced Binary Search Trees. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 40:1-40:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{juge:LIPIcs.WADS.2025.40,
author = {Jug\'{e}, Vincent},
title = {{Grandchildren-Weight-Balanced Binary Search Trees}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {40:1--40:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.40},
URN = {urn:nbn:de:0030-drops-242710},
doi = {10.4230/LIPIcs.WADS.2025.40},
annote = {Keywords: Data structures, Balanced binary trees}
}
Document
Scheduling on Identical Machines with Setup Time and Unknown Execution Time
Abstract
In this study, we investigate a scheduling problem on identical machines in which jobs require initial setup before execution. We assume that an algorithm can dynamically form a batch (i.e., a collection of jobs to be processed together) from the remaining jobs. The setup time is modeled as a known monotone function of the set of jobs within a batch, while the execution time of each job remains unknown until completion. This uncertainty poses significant challenges for minimizing the makespan. We address these challenges by considering two scenarios: each job batch must be assigned to a single machine, or a batch may be distributed across multiple machines. For both scenarios, we analyze settings with and without preemption. Across these four settings, we design online algorithms that achieve asymptotically optimal competitive ratios with respect to both the number of jobs and the number of machines.
Cite as
Yasushi Kawase, Kazuhisa Makino, Vinh Long Phan, and Hanna Sumita. Scheduling on Identical Machines with Setup Time and Unknown Execution Time. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 41:1-41:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{kawase_et_al:LIPIcs.WADS.2025.41,
author = {Kawase, Yasushi and Makino, Kazuhisa and Phan, Vinh Long and Sumita, Hanna},
title = {{Scheduling on Identical Machines with Setup Time and Unknown Execution Time}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {41:1--41:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.41},
URN = {urn:nbn:de:0030-drops-242728},
doi = {10.4230/LIPIcs.WADS.2025.41},
annote = {Keywords: Online scheduling, Competitive analysis, Makespan minimization, Identical machines scheduling}
}
Document
The Parameterized Landscape of Labeled Graph Contractions
Abstract
In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a parameterized complexity point of view, using parameters such as the maximum degree, the degeneracy, the clique-width or treewidth of the input graphs as well as the number of allowed contractions. We put this complexity in perspective with that of the labeled contractibility problem, i.e determining whether a labeled graph is a contraction of another. Surprisingly, our results indicate very little difference between these problems in terms of parameterized complexity status. We only prove their status to differ when parameterizing by both the degeneracy and the number of allowed contractions, showing W[1]-hardness of the maximum common contraction problem in this case, whereas the contractibility problem is FPT.
Cite as
Manuel Lafond and Bertrand Marchand. The Parameterized Landscape of Labeled Graph Contractions. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 42:1-42:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{lafond_et_al:LIPIcs.WADS.2025.42,
author = {Lafond, Manuel and Marchand, Bertrand},
title = {{The Parameterized Landscape of Labeled Graph Contractions}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {42:1--42:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.42},
URN = {urn:nbn:de:0030-drops-242732},
doi = {10.4230/LIPIcs.WADS.2025.42},
annote = {Keywords: Parameterized complexity - contractions - labels - widths}
}
Document
On the Complexity of Finding 1-Center Spanning Trees
Abstract
We consider the problem of finding a spanning tree T of a given undirected graph G such that any other spanning tree can be obtained from T by removing k edges and subsequently adding k edges, where k is minimized over all spanning trees of G. We refer to this minimum k as the treeradius of G.
Treeradius is an interesting graph parameter with natural interpretations: (1) It is the smallest radius of a Hamming ball centered at an extreme point of the spanning tree polytope that covers the entire polytope. (2) Any graph with bounded treeradius also has bounded treewidth. Consequently, if a problem admits a fixed-parameter algorithm parameterized by treewidth, it also admits a fixed-parameter algorithm parameterized by treeradius.
In this paper, we show that computing the exact treeradius for n-vertex graphs requires 2^Ω(n) time under the Exponential Time Hypothesis (ETH) and does not admit a PTAS, with an inapproximability bound of 1153/1152, unless P = NP. This hardness result is surprising, as treeradius has significantly higher ETH complexity compared to analogous problems on shortest path polytopes and star subgraph polytopes.
Cite as
Pin-Hsian Lee, Meng-Tsung Tsai, and Hung-Lung Wang. On the Complexity of Finding 1-Center Spanning Trees. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 43:1-43:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{lee_et_al:LIPIcs.WADS.2025.43,
author = {Lee, Pin-Hsian and Tsai, Meng-Tsung and Wang, Hung-Lung},
title = {{On the Complexity of Finding 1-Center Spanning Trees}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {43:1--43:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.43},
URN = {urn:nbn:de:0030-drops-242743},
doi = {10.4230/LIPIcs.WADS.2025.43},
annote = {Keywords: Treeradius, Spanning tree polytope, Shortest s, t-path polytope}
}
Document
Streaming Algorithms for Conflict-Free Coloring
Abstract
Conflict-free coloring of a hypergraph ℋ = (V,ℰ) using k colors is a function f:V → {1,2, …, k} such that for all E ∈ ℰ, there exists a vertex v ∈ E with a unique color. That is, f(v)≠ f(u) for all u ∈ E ⧵ {v}. The minimum k for which ℋ has a conflict-free coloring using k colors is called the conflict-free chromatic number of ℋ. For a simple graph G, a conflict-free coloring of the hypergraph with vertex set V(G) and edge set being the set of all closed neighborhoods of the vertices in G is called a conflict-free closed neighborhood (CFCN) coloring of G. CFCN chromatic number, denoted by χ_{CN}(G), is the minimum number of colors used in a conflict-free closed neighborhood coloring of G. Analogously, we define conflict-free open neighborhood (CFON) coloring and CFON chromatic number, χ_{ON}(G), of a graph G.
There are various works on proving upper and lower bounds of χ_{ON}(G) and χ_{CN}(G). In this work, we develop streaming algorithms for CFCN and CFON coloring of a graph where the number of colors used matches the best-known upper bounds of χ_{ON}(G) and χi_{CN}(G). Our algorithms use as input an edge stream of the graph G in the insertion-only model. Our results and the best-known bounds for χ_{ON}(G) and χ_{CN}(G) are given below.
1. Pach and Tardos [Combinatorics, Probability and Computing, 2009] showed that, for any n vertex graph G, χ_{CN}(G) = O(ln² n). Glebov, Szabó and Tardos [Combinatorics, Probability and Computing, 2014] showed the existence of graphs G with χ_{CN}(G) = Ω(ln² n). We design a randomized single-pass semi-streaming algorithm (i.e., it uses O(n ln n) space that, given an n-vertex graph G, outputs a CFCN coloring of G using O(ln² n) colors with probability at least (1-2/n).
2. Bhyravarapu, Kalyanasundaram, Mathew [Journal of Graph Theory, 2021] showed that for a graph G with maximum degree Δ, χ_{CN}(G) = O(ln² Δ). The methods used by our algorithms give rise to a simpler, alternate proof for this bound.
3. It is known that χ_{ON}(G) ≤ 1/2 + √{2n + 1/4} (See Pach and Tardos [Combinatorics, Probability and Computing, 2009] and Ph.D. thesis of Cheilaris). This bound is asymptotically tight.
- We design a deterministic single-pass O(n√n) space streaming algorithm that, given a graph G on n vertices, finds a CFON coloring using 2√n colors.
- We design a randomized, single-pass, semi-streaming algorithm to find a CFON coloring of a graph G using O(√n ln² n) colors with success probability at least (1-2/n).
4. It is known that χ_{ON}(G) ≤ Δ+1, where Δ is the maximum degree of a vertex in G. Further, there are graphs G known with χ_{ON}(G) = Δ + 1. We design a randomized two-pass semi-streaming algorithm (uses O(1/(ε²) n ln³ n) space) that outputs a CFON coloring of G using (1+ε)Δ colors, for any ε > 0, with a probability at least (1-1/n).
Cite as
Rogers Mathew, Fahad Panolan, and Seshikanth. Streaming Algorithms for Conflict-Free Coloring. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 44:1-44:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{mathew_et_al:LIPIcs.WADS.2025.44,
author = {Mathew, Rogers and Panolan, Fahad and Seshikanth},
title = {{Streaming Algorithms for Conflict-Free Coloring}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {44:1--44:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.44},
URN = {urn:nbn:de:0030-drops-242756},
doi = {10.4230/LIPIcs.WADS.2025.44},
annote = {Keywords: Streaming algorithm, conflict-free coloring, vertex coloring, randomized algorithms}
}
Document
Fast Kd-Trees for the Kullback-Leibler Divergence and Other Decomposable Bregman Divergences
Abstract
The contributions of the paper span theoretical and implementational results. First, we prove that Kd-trees can be extended to ℝ^d with the distance measured by an arbitrary Bregman divergence. Perhaps surprisingly, this shows that the triangle inequality is not necessary for correct pruning in Kd-trees. Second, we offer an efficient algorithm and C++ implementation for nearest neighbour search for decomposable Bregman divergences.
The implementation supports the Kullback-Leibler divergence (relative entropy) which is a popular distance between probability vectors and is commonly used in statistics and machine learning. This is a step toward broadening the usage of computational geometry algorithms.
Our benchmarks show that our implementation efficiently handles both exact and approximate nearest neighbour queries. Compared to a linear search, we achieve two orders of magnitude speedup for practical scenarios in dimension up to 100. Our solution is simpler and more efficient than competing methods.
Cite as
Tuyen Pham and Hubert Wagner. Fast Kd-Trees for the Kullback-Leibler Divergence and Other Decomposable Bregman Divergences. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 45:1-45:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{pham_et_al:LIPIcs.WADS.2025.45,
author = {Pham, Tuyen and Wagner, Hubert},
title = {{Fast Kd-Trees for the Kullback-Leibler Divergence and Other Decomposable Bregman Divergences}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {45:1--45:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.45},
URN = {urn:nbn:de:0030-drops-242766},
doi = {10.4230/LIPIcs.WADS.2025.45},
annote = {Keywords: Kd-tree, k-d tree, nearest neighbour search, Bregman divergence, decomposable Bregman divergence, KL divergence, relative entropy, cross entropy, Shannon’s entropy}
}
Document
Skipping Ropes: An Efficient Gray Code Algorithm for Generating Wiggly Permutations
Abstract
Wiggly permutations were introduced by Bapat and Pilaud (Wigglyhedron Mathematische Zeitschrift 2025). We positively answer one of their conjectures by finding a Hamilton path in the wiggly flip graph that is isomorphic to the wigglyhedron. Our path provides a Gray code in which successive wiggly permutations are obtained by a single jump or hop, meaning that one or two consecutive symbols move past some number of smaller symbols. The Gray code has a simple greedy description that produces a recursive zig-zag pattern reminiscent of plain changes for permutations. More broadly, our results extend Algorithm J and the series of papers on zig-zag languages initiated by Hartung, Hoang, Mütze and Williams (Combinatorial Generation via Permutation Languages SODA 2020). Finally, we use wiggly changes as the basis for an 𝒪(n)-time delay generation algorithm.
Cite as
Vincent Pilaud and Aaron Williams. Skipping Ropes: An Efficient Gray Code Algorithm for Generating Wiggly Permutations. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{pilaud_et_al:LIPIcs.WADS.2025.46,
author = {Pilaud, Vincent and Williams, Aaron},
title = {{Skipping Ropes: An Efficient Gray Code Algorithm for Generating Wiggly Permutations}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {46:1--46:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.46},
URN = {urn:nbn:de:0030-drops-242778},
doi = {10.4230/LIPIcs.WADS.2025.46},
annote = {Keywords: permutations, wiggly permutations, pattern avoidance, permutahedron, wigglyhedron, Hamilton path, flip graph, Gray code, combinatorial generation, generation algorithm}
}
Document
B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load
Abstract
Uniquely represented (UR) data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of n keys from a totally ordered universe in this context. UR structures are also called "strongly history independent" structures in the literature.
We introduce a two-layer data structure called (α,ε)-Randomized Block Search Tree (RBST) that is uniquely represented and suitable for external memory (EM). Though RBSTs naturally generalize the well-known binary Treaps, several new ideas are needed to analyze the expected search, update, and storage efficiency in terms of block-reads, block-writes, and blocks stored. We prove that searches have O(ε^{-1} + log_α n) block-reads, that dynamic updates perform O(ε^{-1} + log_α(n)/α) block-writes and O(ε^{-2}+(1+(ε^{-1}+log n)/α)log_α n) block-reads, and that (α, ε)-RBSTs have an asymptotic load-factor of at least (1-ε) for every ε ∈ (0,1/2].
Thus (α, ε)-RBSTs improve on the known, uniquely represented B-Treap [Golovin; ICALP'09]. Compared with non-UR structures, the RBST is also, to the best of our knowledge, the first external memory structure that is storage-efficient and has a non-amortized, write-efficient update bound.
Cite as
Roodabeh Safavi and Martin P. Seybold. B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 47:1-47:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{safavi_et_al:LIPIcs.WADS.2025.47,
author = {Safavi, Roodabeh and Seybold, Martin P.},
title = {{B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {47:1--47:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.47},
URN = {urn:nbn:de:0030-drops-242786},
doi = {10.4230/LIPIcs.WADS.2025.47},
annote = {Keywords: Unique Representation, Randomization, Top-Down Analysis, Block Search Tree, Write-Efficiency, Storage-Efficiency}
}
Document
Farthest-Point Voronoi Diagrams in the Hilbert Metric
Abstract
The Hilbert metric, introduced by David Hilbert in 1895, is a projective metric defined on a bounded convex domain in a Euclidean space. For a convex polygon with m vertices and n point sites lying inside the polygon in the plane, it is shown that the nearest-point Voronoi diagram in the Hilbert metric has combinatorial complexity of O(mn) [Gezalyan and Mount, SoCG 2023]. In this paper, we show that the farthest-point Voronoi diagram in the Hilbert metric has combinatorial complexity O(m), which is independent of the number of sites. Also, we present an efficient algorithm to compute the farthest-point Voronoi diagram.
Cite as
Minju Song, Mook Kwon Jung, and Hee-Kap Ahn. Farthest-Point Voronoi Diagrams in the Hilbert Metric. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 48:1-48:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{song_et_al:LIPIcs.WADS.2025.48,
author = {Song, Minju and Jung, Mook Kwon and Ahn, Hee-Kap},
title = {{Farthest-Point Voronoi Diagrams in the Hilbert Metric}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {48:1--48:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.48},
URN = {urn:nbn:de:0030-drops-242797},
doi = {10.4230/LIPIcs.WADS.2025.48},
annote = {Keywords: Farthest-point Voronoi diagram, Hilbert metric, Complexity, Algorithm}
}
Document
On the I/O Complexity of the Cocke-Younger-Kasami Algorithm and of a Family of Related Dynamic Programming Algorithms
Abstract
Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms, including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary search trees. Assuming no recomputation of intermediate values, we establish an Ω(n³/(√M B)) I/O lower bound, where n denotes the size of the input and M denotes the size of the available fast memory (cache). When recomputation is allowed, we show that the same bound holds for M < cn, where c is a positive constant. In the case where M ≥ 2n, we show an Ω(n/B) I/O lower bound. We also discuss algorithms for which the number of executed I/O operations matches asymptotically each of the presented lower bounds, which are thus asymptotically tight.
Additionally, we refine our general method to obtain a lower bound for the I/O complexity of the Cocke-Younger-Kasami algorithm, where the size of the grammar impacts the I/O complexity. An upper bound with asymptotically matching performance in many cases is also provided.
Cite as
Lorenzo De Stefani and Vedant Gupta. On the I/O Complexity of the Cocke-Younger-Kasami Algorithm and of a Family of Related Dynamic Programming Algorithms. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 49:1-49:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{destefani_et_al:LIPIcs.WADS.2025.49,
author = {De Stefani, Lorenzo and Gupta, Vedant},
title = {{On the I/O Complexity of the Cocke-Younger-Kasami Algorithm and of a Family of Related Dynamic Programming Algorithms}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {49:1--49:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.49},
URN = {urn:nbn:de:0030-drops-242800},
doi = {10.4230/LIPIcs.WADS.2025.49},
annote = {Keywords: I/O complexity, Dynamic Programming Algorithms, Lower Bounds, Recomputation, Cocke-Younger-Kasami}
}
Document
Deterministic (2/3 - ε)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries
Abstract
In the matroid intersection problem, we are given two matroids ℳ₁ = (V, ℐ₁) and ℳ₂ = (V, ℐ₂) defined on the same ground set V of n elements, and the objective is to find a common independent set S ∈ ℐ₁ ∩ ℐ₂ of largest possible cardinality, denoted by r. In this paper, we consider a deterministic matroid intersection algorithm with only a nearly linear number of independence oracle queries. Our contribution is to present a deterministic O(n/(ε) + r log r)-independence-query (2/3-ε)-approximation algorithm for any ε > 0. Our idea is very simple: we apply a recent Õ(n √r/ε)-independence-query (1 - ε)-approximation algorithm of Blikstad [ICALP 2021], but terminate it before completion. Moreover, we also present a semi-streaming algorithm for (2/3 -ε)-approximation of matroid intersection in O(1/ε) passes.
Cite as
Tatsuya Terao. Deterministic (2/3 - ε)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{terao:LIPIcs.WADS.2025.50,
author = {Terao, Tatsuya},
title = {{Deterministic (2/3 - \epsilon)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {50:1--50:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.50},
URN = {urn:nbn:de:0030-drops-242812},
doi = {10.4230/LIPIcs.WADS.2025.50},
annote = {Keywords: Matroid intersection, approximation algorithm, streaming algorithm}
}