134 Search Results for "Pagh, Rasmus"

Volume

LIPIcs, Volume 204

29th Annual European Symposium on Algorithms (ESA 2021)

ESA 2021, September 6-8, 2021, Lisbon, Portugal (Virtual Conference)

Editors: Petra Mutzel, Rasmus Pagh, and Grzegorz Herman

Volume

LIPIcs, Volume 53

15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

SWAT 2016, June 22-24, 2016, Reykjavik, Iceland

Editors: Rasmus Pagh

Document
CG Challenge
DOI: 10.4230/LIPIcs.SoCG.2023.66
Constructing Concise Convex Covers via Clique Covers (CG Challenge)

Authors: Mikkel Abrahamsen, William Bille Meyling, and André Nusser

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
This work describes the winning implementation of the CG:SHOP 2023 Challenge. The topic of the Challenge was the convex cover problem: given a polygon P (with holes), find a minimum-cardinality set of convex polygons whose union equals P. We use a three-step approach: (1) Create a suitable partition of P. (2) Compute a visibility graph of the pieces of the partition. (3) Solve a vertex clique cover problem on the visibility graph, from which we then derive the convex cover. This way we capture the geometric difficulty in the first step and the combinatorial difficulty in the third step.
Cite as

Mikkel Abrahamsen, William Bille Meyling, and André Nusser. Constructing Concise Convex Covers via Clique Covers (CG Challenge). In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 66:1-66:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2023.66,
  author =	{Abrahamsen, Mikkel and Bille Meyling, William and Nusser, Andr\'{e}},
  title =	{{Constructing Concise Convex Covers via Clique Covers}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{66:1--66:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.66},
  URN =		{urn:nbn:de:0030-drops-179164},
  doi =		{10.4230/LIPIcs.SoCG.2023.66},
  annote =	{Keywords: Convex cover, Polygons with holes, Algorithm engineering, Vertex clique cover}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.107
Approximate Triangle Counting via Sampling and Fast Matrix Multiplication

Authors: Jakub Tětek

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
There is a simple O(n³/{ε²T}) time algorithm for 1±ε-approximate triangle counting where T is the number of triangles in the graph and n the number of vertices. At the same time, one may count triangles exactly using fast matrix multiplication in time Õ(n^ω). Is it possible to get a negative dependency on the number of triangles T while retaining the state-of-the-art n^ω dependency on n? We answer this question positively by providing an algorithm which runs in time O({n^ω}/T^{ω-2})⋅poly(n^o(1)/ε). This is optimal in the sense that as long as the exponent of T is independent of n, T, it cannot be improved while retaining the dependency on n. Our algorithm improves upon the state of the art when T ≫ 1 and T ≪ n. We also consider the problem of approximate triangle counting in sparse graphs, parameterized by the number of edges m. The best known algorithm runs in time Õ_ε(m^{3/2}/T) [Eden et al., SIAM Journal on Computing, 2017]. An algorithm by Alon et al. [JACM, 1995] for exact triangle counting that runs in time Õ(m^{2ω/(ω + 1)}). We again get an algorithm whose complexity has a state-of-the-art dependency on m while having negative dependency on T. Specifically, our algorithm runs in time O({m^{2ω/(ω+1)}}/{T^{2(ω-1)/(ω+1)}}) ⋅ poly(n^o(1)/ε). This is again optimal in the sense that no better constant exponent of T is possible without worsening the dependency on m. This algorithm improves upon the state of the art when T ≫ 1 and T ≪ √m. In both cases, algorithms with time complexity matching query complexity lower bounds were known on some range of parameters. While those algorithms have optimal query complexity for the whole range of T, the time complexity departs from the query complexity and is no longer optimal (as we show) for T ≪ n and T ≪ √m, respectively. We focus on the time complexity in this range of T. To the best of our knowledge, this is the first paper considering the discrepancy between query and time complexity in graph parameter estimation.
Cite as

Jakub Tětek. Approximate Triangle Counting via Sampling and Fast Matrix Multiplication. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 107:1-107:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{tetek:LIPIcs.ICALP.2022.107,
  author =	{T\v{e}tek, Jakub},
  title =	{{Approximate Triangle Counting via Sampling and Fast Matrix Multiplication}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{107:1--107:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.107},
  URN =		{urn:nbn:de:0030-drops-164485},
  doi =		{10.4230/LIPIcs.ICALP.2022.107},
  annote =	{Keywords: Approximate triangle counting, Fast matrix multiplication, Sampling}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ESA.2021
LIPIcs, Volume 204, ESA 2021, Complete Volume

Authors: Petra Mutzel, Rasmus Pagh, and Grzegorz Herman

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
LIPIcs, Volume 204, ESA 2021, Complete Volume
Cite as

29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 1-1340, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Proceedings{mutzel_et_al:LIPIcs.ESA.2021,
  title =	{{LIPIcs, Volume 204, ESA 2021, Complete Volume}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{1--1340},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021},
  URN =		{urn:nbn:de:0030-drops-145808},
  doi =		{10.4230/LIPIcs.ESA.2021},
  annote =	{Keywords: LIPIcs, Volume 204, ESA 2021, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ESA.2021.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Petra Mutzel, Rasmus Pagh, and Grzegorz Herman

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 0:i-0:xx, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{mutzel_et_al:LIPIcs.ESA.2021.0,
  author =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{0:i--0:xx},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.0},
  URN =		{urn:nbn:de:0030-drops-145816},
  doi =		{10.4230/LIPIcs.ESA.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2021.1
Network Planning and Routing Problems over Time: Models, Complexity and Algorithms (Invited Talk)

Authors: Lukas Glomb, Benno Hoch, Frauke Liers, and Florian Rösel

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
In this invited contribution for ESA 2021, we will study the complexity of and algorithms for network optimization tasks with a timing component. They occur, for example, in planning or routing problems that need to be solved repeatedly over time. Typically, already simplified versions of such problems are NP-hard. In addition, the instances typically are too large to be solved straight-forwardly on a time-expanded graph. After an introduction into the area, we state the problem of determining best possible non-stop trajectories in a network that are not allowed to cross at any point in time. For simplified settings, polynomial-time solution approaches are presented whereas already for restricted settings the problems are shown to be NP-hard. When moving to more complex and more realistic settings as they occur, for example, in determining non-stop disjoint trajectories for a set of aircraft, we present heuristic algorithms that adaptively refine coarse disjoint trajectories in the timing dimension. In order to be able to solve the non-stop disjoint trajectories problem over time, the method is integrated in a rolling-horizon algorithm. We present computational results for realistic settings. Motivated by the fact that rolling-horizon approaches are often applied in practice without knowledge on the quality of the obtained solutions, we study this problem from an abstract point of view. In fact, we more abstractly analyze the solution quality of general rolling-horizon algorithms for optimization tasks that show a timing component. We apply it to different planning problems. We end by pointing out some challenges and possibilities for future research.
Cite as

Lukas Glomb, Benno Hoch, Frauke Liers, and Florian Rösel. Network Planning and Routing Problems over Time: Models, Complexity and Algorithms (Invited Talk). In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 1:1-1:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{glomb_et_al:LIPIcs.ESA.2021.1,
  author =	{Glomb, Lukas and Hoch, Benno and Liers, Frauke and R\"{o}sel, Florian},
  title =	{{Network Planning and Routing Problems over Time: Models, Complexity and Algorithms}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{1:1--1:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.1},
  URN =		{urn:nbn:de:0030-drops-145822},
  doi =		{10.4230/LIPIcs.ESA.2021.1},
  annote =	{Keywords: network problems over time, rolling-horizon, complexity, approximation}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2021.2
A User Friendly Power Tool for Deriving Online Learning Algorithms (Invited Talk)

Authors: Aaron Roth

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
In this talk, we overview a simple and user friendly framework developed in [Noarov et al., 2021] that can be used to derive online learning algorithms in a number of settings. In the core framework, at every round, an adaptive adversary introduces a new game, consisting of an action space for the learner, an action space for the adversary, and a vector valued objective function that is concave-convex in every coordinate. The learner and the adversary then play in this game. The learner’s goal is to play so as to minimize the maximum coordinate of the cumulative vector-valued loss. The resulting one-shot game is not concave-convex, and so the minimax theorem does not apply. Nevertheless we give a simple algorithm that can compete with the setting in which the adversary must announce their action first, with optimally diminishing regret. We demonstrate the power of our simple framework by using it to derive optimal bounds and algorithms across a variety of domains. This includes no regret learning: we can recover optimal algorithms and bounds for minimizing exernal regret, internal regret, adaptive regret, multigroup regret, subsequence regret, and permutation regret in the sleeping experts setting. It also includes (multi)calibration [Hébert-Johnson et al., 2018] and related notions: we are able to recover recently derived algorithms and bounds for online adversarial multicalibration [Gupta et al., 2021], mean conditioned moment multicalibration [Jung et al., 2021], and prediction interval multivalidity [Gupta et al., 2021]. Finally we use it to derive a new variant of Blackwell’s Approachability Theorem, which we term "Fast Polytope Approachability".
Cite as

Aaron Roth. A User Friendly Power Tool for Deriving Online Learning Algorithms (Invited Talk). In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{roth:LIPIcs.ESA.2021.2,
  author =	{Roth, Aaron},
  title =	{{A User Friendly Power Tool for Deriving Online Learning Algorithms}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.2},
  URN =		{urn:nbn:de:0030-drops-145835},
  doi =		{10.4230/LIPIcs.ESA.2021.2},
  annote =	{Keywords: Online Learning, Multicalibration, Multivalidity, Blackwell Approachability}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.3
Bi-Objective Search with Bi-Directional A*

Authors: Saman Ahmadi, Guido Tack, Daniel Harabor, and Philip Kilby

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
Bi-objective search is a well-known algorithmic problem, concerned with finding a set of optimal solutions in a two-dimensional domain. This problem has a wide variety of applications such as planning in transport systems or optimal control in energy systems. Recently, bi-objective A*-based search (BOA*) has shown state-of-the-art performance in large networks. This paper develops a bi-directional and parallel variant of BOA*, enriched with several speed-up heuristics. Our experimental results on 1,000 benchmark cases show that our bi-directional A* algorithm for bi-objective search (BOBA*) can optimally solve all of the benchmark cases within the time limit, outperforming the state of the art BOA*, bi-objective Dijkstra and bi-directional bi-objective Dijkstra by an average runtime improvement of a factor of five over all of the benchmark instances.
Cite as

Saman Ahmadi, Guido Tack, Daniel Harabor, and Philip Kilby. Bi-Objective Search with Bi-Directional A*. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ahmadi_et_al:LIPIcs.ESA.2021.3,
  author =	{Ahmadi, Saman and Tack, Guido and Harabor, Daniel and Kilby, Philip},
  title =	{{Bi-Objective Search with Bi-Directional A*}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.3},
  URN =		{urn:nbn:de:0030-drops-145849},
  doi =		{10.4230/LIPIcs.ESA.2021.3},
  annote =	{Keywords: Bi-objective search, heuristic search, shortest path problem}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.4
A Unified Approach for All Pairs Approximate Shortest Paths in Weighted Undirected Graphs

Authors: Maor Akav and Liam Roditty

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
Let G = (V,E) be a weighted undirected graph with n vertices and m edges, and let d_G(u,v) be the length of the shortest path between u and v in G. In this paper we present a unified approach for obtaining algorithms for all pairs approximate shortest paths in weighted undirected graphs. For every integer k ≥ 2 we show that there is an Õ(n²+kn^{2-3/k}m^{2/k}) expected running time algorithm that computes a matrix M such that for every u,v ∈ V: d_G(u,v) ≤ M[u,v] ≤ (2+(k-2)/k)d_G(u,v). Previous algorithms obtained only specific approximation factors. Baswana and Kavitha [FOCS 2006, SICOMP 2010] presented a 2-approximation algorithm with expected running time of Õ(n²+m√ n) and a 7/3-approximation algorithm with expected running time of Õ(n²+m^{2/3}n). Their results improved upon the results of Cohen and Zwick [SODA 1997, JoA 2001] for graphs with m = o(n²). Kavitha [FSTTCS 2007, Algorithmica 2012] presented a 5/2-approximation algorithm with expected running time of Õ(n^{9/4}). For k = 2 and k = 3 our result gives the algorithms of Baswana and Kavitha. For k = 4, we get a 5/2-approximation algorithm with Õ(n^{5/4}m^{1/2}) expected running time. This improves upon the running time of Õ(n^{9/4}) due to Kavitha, when m = o(n²). Our unified approach reveals that all previous algorithms are a part of a family of algorithms that exhibit a smooth tradeoff between approximation of 2 and 3, and are not sporadic unrelated results. Moreover, our new algorithm uses, among other ideas, the celebrated approximate distance oracles of Thorup and Zwick [STOC 2001, JACM 2005] in a non standard way, which we believe is of independent interest, due to their extensive usage in a variety of applications.
Cite as

Maor Akav and Liam Roditty. A Unified Approach for All Pairs Approximate Shortest Paths in Weighted Undirected Graphs. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{akav_et_al:LIPIcs.ESA.2021.4,
  author =	{Akav, Maor and Roditty, Liam},
  title =	{{A Unified Approach for All Pairs Approximate Shortest Paths in Weighted Undirected Graphs}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.4},
  URN =		{urn:nbn:de:0030-drops-145858},
  doi =		{10.4230/LIPIcs.ESA.2021.4},
  annote =	{Keywords: Graph algorithms, Approximate All Pairs of Shortest Paths, Distance Oracles}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.5
The Voronoi Diagram of Rotating Rays With applications to Floodlight Illumination

Authors: Carlos Alegría, Ioannis Mantas, Evanthia Papadopoulou, Marko Savić, Hendrik Schrezenmaier, Carlos Seara, and Martin Suderland

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We introduce the Voronoi Diagram of Rotating Rays, a Voronoi structure where the input sites are rays, and the distance function is the counterclockwise angular distance between a point and a ray-site. This novel Voronoi diagram is motivated by illumination and coverage problems, where a domain has to be covered by floodlights (wedges) of uniform angle, and the goal is to find the minimum angle necessary to cover the domain. We study the diagram in the plane, and we present structural properties, combinatorial complexity bounds, and a construction algorithm. If the rays are induced by a convex polygon, we show how to construct the ray Voronoi diagram within this polygon in linear time. Using this information, we can find in optimal linear time the Brocard angle, the minimum angle required to illuminate a convex polygon with floodlights of uniform angle. This last algorithm improves upon previous results, settling an interesting open problem.
Cite as

Carlos Alegría, Ioannis Mantas, Evanthia Papadopoulou, Marko Savić, Hendrik Schrezenmaier, Carlos Seara, and Martin Suderland. The Voronoi Diagram of Rotating Rays With applications to Floodlight Illumination. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{alegria_et_al:LIPIcs.ESA.2021.5,
  author =	{Alegr{\'\i}a, Carlos and Mantas, Ioannis and Papadopoulou, Evanthia and Savi\'{c}, Marko and Schrezenmaier, Hendrik and Seara, Carlos and Suderland, Martin},
  title =	{{The Voronoi Diagram of Rotating Rays With applications to Floodlight Illumination}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.5},
  URN =		{urn:nbn:de:0030-drops-145865},
  doi =		{10.4230/LIPIcs.ESA.2021.5},
  annote =	{Keywords: rotating rays, Voronoi diagram, oriented angular distance, Brocard angle, floodlight illumination, coverage problems, art gallery problems}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.6
Parallel Computation of Combinatorial Symmetries

Authors: Markus Anders and Pascal Schweitzer

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the automorphism group of the constructed graph. Such solvers have been developed for over 50 years, and highly efficient sequential, single core tools are available. However no competitive parallel tools are available for the task. We introduce a new parallel randomized algorithm that is based on a modification of the individualization-refinement paradigm used by sequential solvers. The use of randomization crucially enables parallelization. We report extensive benchmark results that show that our solver is competitive to state-of-the-art solvers on a single thread, while scaling remarkably well with the use of more threads. This results in order-of-magnitude improvements on many graph classes over state-of-the-art solvers. In fact, our tool is the first parallel graph automorphism tool that outperforms current sequential tools.
Cite as

Markus Anders and Pascal Schweitzer. Parallel Computation of Combinatorial Symmetries. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{anders_et_al:LIPIcs.ESA.2021.6,
  author =	{Anders, Markus and Schweitzer, Pascal},
  title =	{{Parallel Computation of Combinatorial Symmetries}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.6},
  URN =		{urn:nbn:de:0030-drops-145875},
  doi =		{10.4230/LIPIcs.ESA.2021.6},
  annote =	{Keywords: graph isomorphism, automorphism groups, algorithm engineering, parallel algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.7
Graph Connectivity and Single Element Recovery via Linear and OR Queries

Authors: Sepehr Assadi, Deeparnab Chakrabarty, and Sanjeev Khanna

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We study the problem of finding a spanning forest in an undirected, n-vertex multi-graph under two basic query models. One are Linear queries which are linear measurements on the incidence vector induced by the edges; the other are the weaker OR queries which only reveal whether a given subset of plausible edges is empty or not. At the heart of our study lies a fundamental problem which we call the single element recovery problem: given a non-negative vector x ∈ ℝ^{N}_{≥ 0}, the objective is to return a single element x_j > 0 from the support. Queries can be made in rounds, and our goals is to understand the trade-offs between the query complexity and the rounds of adaptivity needed to solve these problems, for both deterministic and randomized algorithms. These questions have connections and ramifications to multiple areas such as sketching, streaming, graph reconstruction, and compressed sensing. Our main results are as follows: - For the single element recovery problem, it is easy to obtain a deterministic, r-round algorithm which makes (N^{1/r}-1)-queries per-round. We prove that this is tight: any r-round deterministic algorithm must make ≥ (N^{1/r} - 1) Linear queries in some round. In contrast, a 1-round O(polylog)-query randomized algorithm is known to exist. - We design a deterministic O(r)-round, Õ(n^{1+1/r})-OR query algorithm for graph connectivity. We complement this with an Ω̃(n^{1 + 1/r})-lower bound for any r-round deterministic algorithm in the OR-model. - We design a randomized, 2-round algorithm for the graph connectivity problem which makes Õ(n)-OR queries. In contrast, we prove that any 1-round algorithm (possibly randomized) requires Ω̃(n²)-OR queries. A randomized, 1-round algorithm making Õ(n)-Linear queries is already known. All our algorithms, in fact, work with more natural graph query models which are special cases of the above, and have been extensively studied in the literature. These are Cross queries (cut-queries) and BIS (bipartite independent set) queries.
Cite as

Sepehr Assadi, Deeparnab Chakrabarty, and Sanjeev Khanna. Graph Connectivity and Single Element Recovery via Linear and OR Queries. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{assadi_et_al:LIPIcs.ESA.2021.7,
  author =	{Assadi, Sepehr and Chakrabarty, Deeparnab and Khanna, Sanjeev},
  title =	{{Graph Connectivity and Single Element Recovery via Linear and OR Queries}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{7:1--7:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.7},
  URN =		{urn:nbn:de:0030-drops-145880},
  doi =		{10.4230/LIPIcs.ESA.2021.7},
  annote =	{Keywords: Query Models, Graph Connectivity, Group Testing, Duality}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.8
Fully Dynamic Set Cover via Hypergraph Maximal Matching: An Optimal Approximation Through a Local Approach

Authors: Sepehr Assadi and Shay Solomon

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
In the (fully) dynamic set cover problem, we have a collection of m sets from a universe of size n that undergo element insertions and deletions; the goal is to maintain an approximate set cover of the universe after each update. We give an O(f²) update time algorithm for this problem that achieves an f-approximation, where f is the maximum number of sets that an element belongs to; under the unique games conjecture, this approximation is best possible for any fixed f. This is the first algorithm for dynamic set cover with approximation ratio that exactly matches f (as opposed to almost f in prior work), as well as the first one with runtime independent of n,m (for any approximation factor of o(f³)). Prior to our work, the state-of-the-art algorithms for this problem were O(f²) update time algorithms of Gupta et al. [STOC'17] and Bhattacharya et al. [IPCO'17] with O(f³) approximation, and the recent algorithm of Bhattacharya {et al. } [FOCS'19] with O(f⋅log{n}/ε²) update time and (1+ε)⋅f approximation, improving the O(f²⋅log{n}/ε⁵) bound of Abboud et al. [STOC'19]. The key technical ingredient of our work is an algorithm for maintaining a maximal matching in a dynamic hypergraph of rank r - where each hyperedge has at most r vertices - that undergoes hyperedge insertions and deletions in O(r²) amortized update time; our algorithm is randomized, and the bound on the update time holds in expectation and with high probability. This result generalizes the maximal matching algorithm of Solomon [FOCS'16] with constant update time in ordinary graphs to hypergraphs, and is of independent merit; the previous state-of-the-art algorithms for set cover do not translate to (integral) matchings for hypergraphs, let alone a maximal one. Our quantitative result for the set cover problem is translated directly from this qualitative result for maximal matching using standard reductions. An important advantage of our approach over the previous ones for approximation (1+ε)⋅f (by Abboud et al. [STOC'19] and Bhattacharya et al. [FOCS'19]) is that it is inherently local and can thus be distributed efficiently to achieve low amortized round and message complexities.
Cite as

Sepehr Assadi and Shay Solomon. Fully Dynamic Set Cover via Hypergraph Maximal Matching: An Optimal Approximation Through a Local Approach. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{assadi_et_al:LIPIcs.ESA.2021.8,
  author =	{Assadi, Sepehr and Solomon, Shay},
  title =	{{Fully Dynamic Set Cover via Hypergraph Maximal Matching: An Optimal Approximation Through a Local Approach}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.8},
  URN =		{urn:nbn:de:0030-drops-145899},
  doi =		{10.4230/LIPIcs.ESA.2021.8},
  annote =	{Keywords: dynamic graph algorithms, hypergraph, maximal matching, matching, set cover}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.9
The Randomized Competitive Ratio of Weighted k-Server Is at Least Exponential

Authors: Nikhil Ayyadevara and Ashish Chiplunkar

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
The weighted k-server problem is a natural generalization of the k-server problem in which the cost incurred in moving a server is the distance traveled times the weight of the server. Even after almost three decades since the seminal work of Fiat and Ricklin (1994), the competitive ratio of this problem remains poorly understood even on the simplest class of metric spaces - the uniform metric spaces. In particular, in the case of randomized algorithms against the oblivious adversary, neither a better upper bound that the doubly exponential deterministic upper bound, nor a better lower bound than the logarithmic lower bound of unweighted k-server, is known. In this paper, we make significant progress towards understanding the randomized competitive ratio of weighted k-server on uniform metrics. We cut down the triply exponential gap between the upper and lower bound to a singly exponential gap by proving that the competitive ratio is at least exponential in k, substantially improving on the previously known lower bound of about ln k.
Cite as

Nikhil Ayyadevara and Ashish Chiplunkar. The Randomized Competitive Ratio of Weighted k-Server Is at Least Exponential. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 9:1-9:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{ayyadevara_et_al:LIPIcs.ESA.2021.9,
  author =	{Ayyadevara, Nikhil and Chiplunkar, Ashish},
  title =	{{The Randomized Competitive Ratio of Weighted k-Server Is at Least Exponential}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{9:1--9:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.9},
  URN =		{urn:nbn:de:0030-drops-145904},
  doi =		{10.4230/LIPIcs.ESA.2021.9},
  annote =	{Keywords: weighted k-server, competitive analysis}
}
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