83 Search Results for "Even, Guy"


Document
On the Uncrossed Number of Graphs

Authors: Martin Balko, Petr Hliněný, Tomáš Masařík, Joachim Orthaber, Birgit Vogtenhuber, and Mirko H. Wagner

Published in: LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)


Abstract
Visualizing a graph G in the plane nicely, for example, without crossings, is unfortunately not always possible. To address this problem, Masařík and Hliněný [GD 2023] recently asked for each edge of G to be drawn without crossings while allowing multiple different drawings of G. More formally, a collection 𝒟 of drawings of G is uncrossed if, for each edge e of G, there is a drawing in 𝒟 such that e is uncrossed. The uncrossed number unc(G) of G is then the minimum number of drawings in some uncrossed collection of G. No exact values of the uncrossed numbers have been determined yet, not even for simple graph classes. In this paper, we provide the exact values for uncrossed numbers of complete and complete bipartite graphs, partly confirming and partly refuting a conjecture posed by Hliněný and Masařík [GD 2023]. We also present a strong general lower bound on unc(G) in terms of the number of vertices and edges of G. Moreover, we prove NP-hardness of the related problem of determining the edge crossing number of a graph G, which is the smallest number of edges of G taken over all drawings of G that participate in a crossing. This problem was posed as open by Schaefer in his book [Crossing Numbers of Graphs 2018].

Cite as

Martin Balko, Petr Hliněný, Tomáš Masařík, Joachim Orthaber, Birgit Vogtenhuber, and Mirko H. Wagner. On the Uncrossed Number of Graphs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{balko_et_al:LIPIcs.GD.2024.18,
  author =	{Balko, Martin and Hlin\v{e}n\'{y}, Petr and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Orthaber, Joachim and Vogtenhuber, Birgit and Wagner, Mirko H.},
  title =	{{On the Uncrossed Number of Graphs}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.18},
  URN =		{urn:nbn:de:0030-drops-213028},
  doi =		{10.4230/LIPIcs.GD.2024.18},
  annote =	{Keywords: Uncrossed Number, Crossing Number, Planarity, Thickness}
}
Document
A Knowledge-Based Analysis of Intersection Protocols

Authors: Kaya Alpturer, Joseph Y. Halpern, and Ron van der Meyden

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)


Abstract
The increasing wireless communication capabilities of vehicles creates opportunities for more efficient intersection management strategies. One promising approach is the replacement of traffic lights with a system wherein vehicles run protocols among themselves to determine right of way. In this paper, we define the intersection problem to model this scenario abstractly, without any assumptions on the specific structure of the intersection or a bound on the number of vehicles. Protocols solving the intersection problem must guarantee safety (no collisions) and liveness (every vehicle eventually goes through). In addition, we would like these protocols to satisfy various optimality criteria, some of which turn out to be achievable only in a subset of the contexts. In particular, we show a partial equivalence between eliminating unnecessary waiting, a criterion of interest in the distributed mutual-exclusion literature, and a notion of optimality that we define called lexicographical optimality. We then introduce a framework to design protocols for the intersection problem by converting an intersection policy, which is based on a global view of the intersection, to a protocol that can be run by the vehicles through the use of knowledge-based programs. Our protocols are shown to guarantee safety and liveness while also being optimal under sufficient conditions on the context. Finally, we investigate protocols in the presence of faulty vehicles that experience communication failures and older vehicles with limited communication capabilities. We show that intersection protocols can be made safe, live and optimal even in the presence of faulty behavior.

Cite as

Kaya Alpturer, Joseph Y. Halpern, and Ron van der Meyden. A Knowledge-Based Analysis of Intersection Protocols. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{alpturer_et_al:LIPIcs.DISC.2024.2,
  author =	{Alpturer, Kaya and Halpern, Joseph Y. and van der Meyden, Ron},
  title =	{{A Knowledge-Based Analysis of Intersection Protocols}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{2:1--2:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.2},
  URN =		{urn:nbn:de:0030-drops-212291},
  doi =		{10.4230/LIPIcs.DISC.2024.2},
  annote =	{Keywords: Intersection management, Autonomous vehicles, Distributed algorithms, Epistemic logic, Fault tolerance}
}
Document
Parallel Set Cover and Hypergraph Matching via Uniform Random Sampling

Authors: Laxman Dhulipala, Michael Dinitz, Jakub Łącki, and Slobodan Mitrović

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)


Abstract
The SetCover problem has been extensively studied in many different models of computation, including parallel and distributed settings. From an approximation point of view, there are two standard guarantees: an O(log Δ)-approximation (where Δ is the maximum set size) and an O(f)-approximation (where f is the maximum number of sets containing any given element). In this paper, we introduce a new, surprisingly simple, model-independent approach to solving SetCover in unweighted graphs. We obtain multiple improved algorithms in the MPC and CRCW PRAM models. First, in the MPC model with sublinear space per machine, our algorithms can compute an O(f) approximation to SetCover in Ô(√{log Δ} + log f) rounds and a O(log Δ) approximation in O(log^{3/2} n) rounds. Moreover, in the PRAM model, we give a O(f) approximate algorithm using linear work and O(log n) depth. All these bounds improve the existing round complexity/depth bounds by a log^{Ω(1)} n factor. Moreover, our approach leads to many other new algorithms, including improved algorithms for the HypergraphMatching problem in the MPC model, as well as simpler SetCover algorithms that match the existing bounds.

Cite as

Laxman Dhulipala, Michael Dinitz, Jakub Łącki, and Slobodan Mitrović. Parallel Set Cover and Hypergraph Matching via Uniform Random Sampling. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 19:1-19:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{dhulipala_et_al:LIPIcs.DISC.2024.19,
  author =	{Dhulipala, Laxman and Dinitz, Michael and {\L}\k{a}cki, Jakub and Mitrovi\'{c}, Slobodan},
  title =	{{Parallel Set Cover and Hypergraph Matching via Uniform Random Sampling}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{19:1--19:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.19},
  URN =		{urn:nbn:de:0030-drops-212453},
  doi =		{10.4230/LIPIcs.DISC.2024.19},
  annote =	{Keywords: approximate maximum matching, set cover, hypergraph matching, PRAM, massively parallel computation}
}
Document
Massively Parallel Ruling Set Made Deterministic

Authors: Jeff Giliberti and Zahra Parsaeian

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)


Abstract
We study the deterministic complexity of the 2-Ruling Set problem in the model of Massively Parallel Computation (MPC) with linear and strongly sublinear local memory. - Linear MPC: We present a constant-round deterministic algorithm for the 2-Ruling Set problem that matches the randomized round complexity recently settled by Cambus, Kuhn, Pai, and Uitto [DISC'23], and improves upon the deterministic O(log log n)-round algorithm by Pai and Pemmaraju [PODC'22]. Our main ingredient is a simpler analysis of CKPU’s algorithm based solely on bounded independence, which makes its efficient derandomization possible. - Sublinear MPC: We present a deterministic algorithm that computes a 2-Ruling Set in Õ(√{log n}) rounds deterministically. Notably, this is the first deterministic ruling set algorithm with sublogarithmic round complexity, improving on the O(log Δ + log log^* n)-round complexity that stems from the deterministic MIS algorithm of Czumaj, Davies, and Parter [TALG'21]. Our result is based on a simple and fast randomness-efficient construction that achieves the same sparsification as that of the randomized Õ(√{log n})-round LOCAL algorithm by Kothapalli and Pemmaraju [FSTTCS'12].

Cite as

Jeff Giliberti and Zahra Parsaeian. Massively Parallel Ruling Set Made Deterministic. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 29:1-29:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{giliberti_et_al:LIPIcs.DISC.2024.29,
  author =	{Giliberti, Jeff and Parsaeian, Zahra},
  title =	{{Massively Parallel Ruling Set Made Deterministic}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{29:1--29:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.29},
  URN =		{urn:nbn:de:0030-drops-212551},
  doi =		{10.4230/LIPIcs.DISC.2024.29},
  annote =	{Keywords: deterministic algorithms, distributed computing, massively parallel computation, graph algorithms, derandomization}
}
Document
Online Flexible Busy Time Scheduling on Heterogeneous Machines

Authors: Gruia Călinescu, Sami Davies, Samir Khuller, and Shirley Zhang

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)


Abstract
We study the online busy time scheduling model on heterogeneous machines. In our setting, jobs with uniform length arrive online with a deadline that becomes known to the algorithm at the job’s arrival time. An algorithm has access to machines, each with different associated capacities and costs. The goal is to schedule jobs on machines by their deadline, so that the total cost incurred by the scheduling algorithm is minimized. While busy time scheduling has been well-studied, relatively little is known when machines are heterogeneous (i.e., have different costs and capacities), despite this natural theoretical generalization being the most practical model for clients using cloud computing services. We make significant progress in understanding this model by designing an 8-competitive algorithm for the problem on unit-length jobs and provide a lower bound of 2 on the competitive ratio. The lower bound is tight in the setting when jobs form non-nested intervals. Our 8-competitive algorithm generalizes to one with competitive ratio 8(2p-1)/p < 16 when all jobs have uniform length p.

Cite as

Gruia Călinescu, Sami Davies, Samir Khuller, and Shirley Zhang. Online Flexible Busy Time Scheduling on Heterogeneous Machines. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{calinescu_et_al:LIPIcs.ESA.2024.37,
  author =	{C\u{a}linescu, Gruia and Davies, Sami and Khuller, Samir and Zhang, Shirley},
  title =	{{Online Flexible Busy Time Scheduling on Heterogeneous Machines}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{37:1--37:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.37},
  URN =		{urn:nbn:de:0030-drops-211083},
  doi =		{10.4230/LIPIcs.ESA.2024.37},
  annote =	{Keywords: Online algorithms, Scheduling, Competitive analysis}
}
Document
Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing

Authors: Chandra Chekuri and Rhea Jain

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)


Abstract
We consider two-cost network design models in which edges of the input graph have an associated cost and length. We build upon recent advances in hop-constrained oblivious routing to obtain two sets of results. We address multicommodity buy-at-bulk network design in the nonuniform setting. Existing poly-logarithmic approximations are based on the junction tree approach [Chekuri et al., 2010; Guy Kortsarz and Zeev Nutov, 2011]. We obtain a new polylogarithmic approximation via a natural LP relaxation. This establishes an upper bound on its integrality gap and affirmatively answers an open question raised in [Chekuri et al., 2010]. The rounding is based on recent results in hop-constrained oblivious routing [Ghaffari et al., 2021], and this technique yields a polylogarithmic approximation in more general settings such as set connectivity. Our algorithm for buy-at-bulk network design is based on an LP-based reduction to h-hop constrained network design for which we obtain LP-based bicriteria approximation algorithms. We also consider a fault-tolerant version of h-hop constrained network design where one wants to design a low-cost network to guarantee short paths between a given set of source-sink pairs even when k-1 edges can fail. This model has been considered in network design [Luis Gouveia and Markus Leitner, 2017; Gouveia et al., 2018; Arslan et al., 2020] but no approximation algorithms were known. We obtain polylogarithmic bicriteria approximation algorithms for the single-source setting for any fixed k. We build upon the single-source algorithm and the junction-tree approach to obtain an approximation algorithm for the multicommodity setting when at most one edge can fail.

Cite as

Chandra Chekuri and Rhea Jain. Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 41:1-41:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{chekuri_et_al:LIPIcs.ESA.2024.41,
  author =	{Chekuri, Chandra and Jain, Rhea},
  title =	{{Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{41:1--41:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.41},
  URN =		{urn:nbn:de:0030-drops-211124},
  doi =		{10.4230/LIPIcs.ESA.2024.41},
  annote =	{Keywords: Buy-at-bulk, Hop-constrained network design, LP integrality gap, Fault-tolerant network design}
}
Document
From Directed Steiner Tree to Directed Polymatroid Steiner Tree in Planar Graphs

Authors: Chandra Chekuri, Rhea Jain, Shubhang Kulkarni, Da Wei Zheng, and Weihao Zhu

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)


Abstract
In the Directed Steiner Tree (DST) problem the input is a directed edge-weighted graph G = (V,E), a root vertex r and a set S ⊆ V of k terminals. The goal is to find a min-cost subgraph that connects r to each of the terminals. DST admits an O(log² k/log log k)-approximation in quasi-polynomial time [Grandoni et al., 2022; Rohan Ghuge and Viswanath Nagarajan, 2022], and an O(k^{ε})-approximation for any fixed ε > 0 in polynomial-time [Alexander Zelikovsky, 1997; Moses Charikar et al., 1999]. Resolving the existence of a polynomial-time poly-logarithmic approximation is a major open problem in approximation algorithms. In a recent work, Friggstad and Mousavi [Zachary Friggstad and Ramin Mousavi, 2023] obtained a simple and elegant polynomial-time O(log k)-approximation for DST in planar digraphs via Thorup’s shortest path separator theorem [Thorup, 2004]. We build on their work and obtain several new results on DST and related problems. - We develop a tree embedding technique for rooted problems in planar digraphs via an interpretation of the recursion in [Zachary Friggstad and Ramin Mousavi, 2023]. Using this we obtain polynomial-time poly-logarithmic approximations for Group Steiner Tree [Naveen Garg et al., 2000], Covering Steiner Tree [Goran Konjevod et al., 2002] and the Polymatroid Steiner Tree [Gruia Călinescu and Alexander Zelikovsky, 2005] problems in planar digraphs. All these problems are hard to approximate to within a factor of Ω(log² n/log log n) even in trees [Eran Halperin and Robert Krauthgamer, 2003; Grandoni et al., 2022]. - We prove that the natural cut-based LP relaxation for DST has an integrality gap of O(log² k) in planar digraphs. This is in contrast to general graphs where the integrality gap of this LP is known to be Ω(√k) [Leonid Zosin and Samir Khuller, 2002] and Ω(n^{δ}) for some fixed δ > 0 [Shi Li and Bundit Laekhanukit, 2022]. - We combine the preceding results with density based arguments to obtain poly-logarithmic approximations for the multi-rooted versions of the problems in planar digraphs. For DST our result improves the O(R + log k) approximation of [Zachary Friggstad and Ramin Mousavi, 2023] when R = ω(log² k).

Cite as

Chandra Chekuri, Rhea Jain, Shubhang Kulkarni, Da Wei Zheng, and Weihao Zhu. From Directed Steiner Tree to Directed Polymatroid Steiner Tree in Planar Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 42:1-42:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{chekuri_et_al:LIPIcs.ESA.2024.42,
  author =	{Chekuri, Chandra and Jain, Rhea and Kulkarni, Shubhang and Zheng, Da Wei and Zhu, Weihao},
  title =	{{From Directed Steiner Tree to Directed Polymatroid Steiner Tree in Planar Graphs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{42:1--42:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.42},
  URN =		{urn:nbn:de:0030-drops-211134},
  doi =		{10.4230/LIPIcs.ESA.2024.42},
  annote =	{Keywords: Directed Planar Graphs, Submodular Functions, Steiner Tree, Network Design}
}
Document
An Optimal Randomized Algorithm for Finding the Saddlepoint

Authors: Justin Dallant, Frederik Haagensen, Riko Jacob, László Kozma, and Sebastian Wild

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)


Abstract
A saddlepoint of an n × n matrix is an entry that is the maximum of its row and the minimum of its column. Saddlepoints give the value of a two-player zero-sum game, corresponding to its pure-strategy Nash equilibria; efficiently finding a saddlepoint is thus a natural and fundamental algorithmic task. For finding a strict saddlepoint (an entry that is the strict maximum of its row and the strict minimum of its column) an O(n log* n)-time algorithm was recently obtained by Dallant, Haagensen, Jacob, Kozma, and Wild, improving the O(n log n) bounds from 1991 of Bienstock, Chung, Fredman, Schäffer, Shor, Suri and of Byrne and Vaserstein. In this paper we present an optimal O(n)-time algorithm for finding a strict saddlepoint based on random sampling. Our algorithm, like earlier approaches, accesses matrix entries only via unit-cost binary comparisons. For finding a (non-strict) saddlepoint, we extend an existing lower bound to randomized algorithms, showing that the trivial O(n²) runtime cannot be improved even with the use of randomness.

Cite as

Justin Dallant, Frederik Haagensen, Riko Jacob, László Kozma, and Sebastian Wild. An Optimal Randomized Algorithm for Finding the Saddlepoint. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 44:1-44:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{dallant_et_al:LIPIcs.ESA.2024.44,
  author =	{Dallant, Justin and Haagensen, Frederik and Jacob, Riko and Kozma, L\'{a}szl\'{o} and Wild, Sebastian},
  title =	{{An Optimal Randomized Algorithm for Finding the Saddlepoint}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{44:1--44:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.44},
  URN =		{urn:nbn:de:0030-drops-211154},
  doi =		{10.4230/LIPIcs.ESA.2024.44},
  annote =	{Keywords: saddlepoint, matrix, comparison, search, randomized algorithms}
}
Document
Invertible Bloom Lookup Tables with Less Memory and Randomness

Authors: Nils Fleischhacker, Kasper Green Larsen, Maciej Obremski, and Mark Simkin

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)


Abstract
In this work we study Invertible Bloom Lookup Tables (IBLTs) with small failure probabilities. IBLTs are highly versatile data structures that have found applications in set reconciliation protocols, error-correcting codes, and even the design of advanced cryptographic primitives. For storing n elements and ensuring correctness with probability at least 1 - δ, existing IBLT constructions require Ω(n((log(1/δ))/(log n))+1)) space and they crucially rely on fully random hash functions. We present new constructions of IBLTs that are simultaneously more space efficient and require less randomness. For storing n elements with a failure probability of at most δ, our data structure only requires O{n + log(1/δ)log log(1/δ)} space and O{log(log(n)/δ)}-wise independent hash functions. As a key technical ingredient we show that hashing n keys with any k-wise independent hash function h:U → [Cn] for some sufficiently large constant C guarantees with probability 1 - 2^{-Ω(k)} that at least n/2 keys will have a unique hash value. Proving this is non-trivial as k approaches n. We believe that the techniques used to prove this statement may be of independent interest. We apply our new IBLTs to the encrypted compression problem, recently studied by Fleischhacker, Larsen, Simkin (Eurocrypt 2023). We extend their approach to work for a more general class of encryption schemes and using our new IBLT we achieve an asymptotically better compression rate.

Cite as

Nils Fleischhacker, Kasper Green Larsen, Maciej Obremski, and Mark Simkin. Invertible Bloom Lookup Tables with Less Memory and Randomness. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 54:1-54:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{fleischhacker_et_al:LIPIcs.ESA.2024.54,
  author =	{Fleischhacker, Nils and Larsen, Kasper Green and Obremski, Maciej and Simkin, Mark},
  title =	{{Invertible Bloom Lookup Tables with Less Memory and Randomness}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{54:1--54:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.54},
  URN =		{urn:nbn:de:0030-drops-211252},
  doi =		{10.4230/LIPIcs.ESA.2024.54},
  annote =	{Keywords: Invertible Bloom Lookup Tables}
}
Document
Random-Order Online Independent Set of Intervals and Hyperrectangles

Authors: Mohit Garg, Debajyoti Kar, and Arindam Khan

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)


Abstract
In the Maximum Independent Set of Hyperrectangles problem, we are given a set of n (possibly overlapping) d-dimensional axis-aligned hyperrectangles, and the goal is to find a subset of non-overlapping hyperrectangles of maximum cardinality. For d = 1, this corresponds to the classical Interval Scheduling problem, where a simple greedy algorithm returns an optimal solution. In the offline setting, for d-dimensional hyperrectangles, polynomial time (log n)^{O(d)}-approximation algorithms are known [Chalermsook and Chuzhoy, 2009]. However, the problem becomes notably challenging in the online setting, where the input objects (hyperrectangles) appear one by one in an adversarial order, and on the arrival of an object, the algorithm needs to make an immediate and irrevocable decision whether or not to select the object while maintaining the feasibility. Even for interval scheduling, an Ω(n) lower bound is known on the competitive ratio. To circumvent these negative results, in this work, we study the online maximum independent set of axis-aligned hyperrectangles in the random-order arrival model, where the adversary specifies the set of input objects which then arrive in a uniformly random order. Starting from the prototypical secretary problem, the random-order model has received significant attention to study algorithms beyond the worst-case competitive analysis (see the survey by Gupta and Singla [Anupam Gupta and Sahil Singla, 2020]). Surprisingly, we show that the problem in the random-order model almost matches the best-known offline approximation guarantees, up to polylogarithmic factors. In particular, we give a simple (log n)^{O(d)}-competitive algorithm for d-dimensional hyperrectangles in this model, which runs in O_d̃(n) time. Our approach also yields (log n)^{O(d)}-competitive algorithms in the random-order model for more general objects such as d-dimensional fat objects and ellipsoids. Furthermore, all our competitiveness guarantees hold with high probability, and not just in expectation.

Cite as

Mohit Garg, Debajyoti Kar, and Arindam Khan. Random-Order Online Independent Set of Intervals and Hyperrectangles. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 58:1-58:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{garg_et_al:LIPIcs.ESA.2024.58,
  author =	{Garg, Mohit and Kar, Debajyoti and Khan, Arindam},
  title =	{{Random-Order Online Independent Set of Intervals and Hyperrectangles}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{58:1--58:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.58},
  URN =		{urn:nbn:de:0030-drops-211298},
  doi =		{10.4230/LIPIcs.ESA.2024.58},
  annote =	{Keywords: Online Algorithms, Random-Order Model, Maximum Independent Set of Rectangles, Hyperrectangles, Fat Objects, Interval Scheduling}
}
Document
Locally Computing Edge Orientations

Authors: Slobodan Mitrović, Ronitt Rubinfeld, and Mihir Singhal

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)


Abstract
We consider the question of orienting the edges in a graph G such that every vertex has bounded out-degree. For graphs of arboricity α, there is an orientation in which every vertex has out-degree at most α and, moreover, the best possible maximum out-degree of an orientation is at least α - 1. We are thus interested in algorithms that can achieve a maximum out-degree of close to α. A widely studied approach for this problem in the distributed algorithms setting is a "peeling algorithm" that provides an orientation with maximum out-degree α(2+ε) in a logarithmic number of iterations. We consider this problem in the local computation algorithm (LCA) model, which quickly answers queries of the form "What is the orientation of edge (u,v)?" by probing the input graph. When the peeling algorithm is executed in the LCA setting by applying standard techniques, e.g., the Parnas-Ron paradigm, it requires Ω(n) probes per query on an n-vertex graph. In the case where G has unbounded degree, we show that any LCA that orients its edges to yield maximum out-degree r must use Ω(√ n/r) probes to G per query in the worst case, even if G is known to be a forest (that is, α = 1). We also show several algorithms with sublinear probe complexity when G has unbounded degree. When G is a tree such that the maximum degree Δ of G is bounded, we demonstrate an algorithm that uses Δ n^{1-log_Δ r + o(1)} probes to G per query. To obtain this result, we develop an edge-coloring approach that ultimately yields a graph-shattering-like result. We also use this shattering-like approach to demonstrate an LCA which 4-colors any tree using sublinear probes per query.

Cite as

Slobodan Mitrović, Ronitt Rubinfeld, and Mihir Singhal. Locally Computing Edge Orientations. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 89:1-89:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{mitrovic_et_al:LIPIcs.ESA.2024.89,
  author =	{Mitrovi\'{c}, Slobodan and Rubinfeld, Ronitt and Singhal, Mihir},
  title =	{{Locally Computing Edge Orientations}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{89:1--89:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.89},
  URN =		{urn:nbn:de:0030-drops-211603},
  doi =		{10.4230/LIPIcs.ESA.2024.89},
  annote =	{Keywords: local computation algorithms, edge orientation, tree coloring}
}
Document
APPROX
Online Time-Windows TSP with Predictions

Authors: Shuchi Chawla and Dimitris Christou

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)


Abstract
In the Time-Windows TSP (TW-TSP) we are given requests at different locations on a network; each request is endowed with a reward and an interval of time; the goal is to find a tour that visits as much reward as possible during the corresponding time window. For the online version of this problem, where each request is revealed at the start of its time window, no finite competitive ratio can be obtained. We consider a version of the problem where the algorithm is presented with predictions of where and when the online requests will appear, without any knowledge of the quality of this side information. Vehicle routing problems such as the TW-TSP can be very sensitive to errors or changes in the input due to the hard time-window constraints, and it is unclear whether imperfect predictions can be used to obtain a finite competitive ratio. We show that good performance can be achieved by explicitly building slack into the solution. Our main result is an online algorithm that achieves a competitive ratio logarithmic in the diameter of the underlying network, matching the performance of the best offline algorithm to within factors that depend on the quality of the provided predictions. The competitive ratio degrades smoothly as a function of the quality and we show that this dependence is tight within constant factors.

Cite as

Shuchi Chawla and Dimitris Christou. Online Time-Windows TSP with Predictions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{chawla_et_al:LIPIcs.APPROX/RANDOM.2024.2,
  author =	{Chawla, Shuchi and Christou, Dimitris},
  title =	{{Online Time-Windows TSP with Predictions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{2:1--2:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.2},
  URN =		{urn:nbn:de:0030-drops-209954},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.2},
  annote =	{Keywords: Travelling Salesman Problem, Predictions, Learning-Augmented Algorithms, Approximation}
}
Document
APPROX
Bipartizing (Pseudo-)Disk Graphs: Approximation with a Ratio Better than 3

Authors: Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Jie Xue, and Meirav Zehavi

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)


Abstract
In a disk graph, every vertex corresponds to a disk in ℝ² and two vertices are connected by an edge whenever the two corresponding disks intersect. Disk graphs form an important class of geometric intersection graphs, which generalizes both planar graphs and unit-disk graphs. We study a fundamental optimization problem in algorithmic graph theory, Bipartization (also known as Odd Cycle Transversal), on the class of disk graphs. The goal of Bipartization is to delete a minimum number of vertices from the input graph such that the resulting graph is bipartite. A folklore (polynomial-time) 3-approximation algorithm for Bipartization on disk graphs follows from the classical framework of Goemans and Williamson [Combinatorica'98] for cycle-hitting problems. For over two decades, this result has remained the best known approximation for the problem (in fact, even for Bipartization on unit-disk graphs). In this paper, we achieve the first improvement upon this result, by giving a (3-α)-approximation algorithm for Bipartization on disk graphs, for some constant α > 0. Our algorithm directly generalizes to the broader class of pseudo-disk graphs. Furthermore, our algorithm is robust in the sense that it does not require a geometric realization of the input graph to be given.

Cite as

Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Jie Xue, and Meirav Zehavi. Bipartizing (Pseudo-)Disk Graphs: Approximation with a Ratio Better than 3. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{lokshtanov_et_al:LIPIcs.APPROX/RANDOM.2024.6,
  author =	{Lokshtanov, Daniel and Panolan, Fahad and Saurabh, Saket and Xue, Jie and Zehavi, Meirav},
  title =	{{Bipartizing (Pseudo-)Disk Graphs: Approximation with a Ratio Better than 3}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.6},
  URN =		{urn:nbn:de:0030-drops-209990},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.6},
  annote =	{Keywords: bipartization, geometric intersection graphs, approximation algorithms}
}
Document
APPROX
Distributional Online Weighted Paging with Limited Horizon

Authors: Yaron Fairstein, Joseph (Seffi) Naor, and Tomer Tsachor

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)


Abstract
In this work we study the classic problem of online weighted paging with a probabilistic prediction model, in which we are given additional information about the input in the form of distributions over page requests, known as distributional online paging (DOP). This work continues a recent line of research on learning-augmented algorithms that incorporates machine-learning predictions in online algorithms, so as to go beyond traditional worst-case competitive analysis, thus circumventing known lower bounds for online paging. We first provide an efficient online algorithm that achieves a constant factor competitive ratio with respect to the best online algorithm (policy) for weighted DOP that follows from earlier work on the stochastic k-server problem. Our main contribution concerns the question of whether distributional information over a limited horizon suffices for obtaining a constant competitive factor. To this end, we define in a natural way a new predictive model with limited horizon, which we call Per-Request Stochastic Prediction (PRSP). We show that we can obtain a constant factor competitive algorithm with respect to the optimal online algorithm for this model.

Cite as

Yaron Fairstein, Joseph (Seffi) Naor, and Tomer Tsachor. Distributional Online Weighted Paging with Limited Horizon. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{fairstein_et_al:LIPIcs.APPROX/RANDOM.2024.15,
  author =	{Fairstein, Yaron and Naor, Joseph (Seffi) and Tsachor, Tomer},
  title =	{{Distributional Online Weighted Paging with Limited Horizon}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.15},
  URN =		{urn:nbn:de:0030-drops-210088},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.15},
  annote =	{Keywords: Online algorithms, Caching, Stochastic analysis, Predictions}
}
Document
APPROX
Competitive Query Minimization for Stable Matching with One-Sided Uncertainty

Authors: Evripidis Bampis, Konstantinos Dogeas, Thomas Erlebach, Nicole Megow, Jens Schlöter, and Amitabh Trehan

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)


Abstract
We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are unknown. An algorithm can make queries to reveal information about the preferences of the agents in B. We examine three query models: comparison queries, interviews, and set queries. Using competitive analysis, our aim is to design algorithms that minimize the number of queries required to solve the problem of finding a stable matching or verifying that a given matching is stable (or stable and optimal for the agents of one side). We present various upper and lower bounds on the best possible competitive ratio as well as results regarding the complexity of the offline problem of determining the optimal query set given full information.

Cite as

Evripidis Bampis, Konstantinos Dogeas, Thomas Erlebach, Nicole Megow, Jens Schlöter, and Amitabh Trehan. Competitive Query Minimization for Stable Matching with One-Sided Uncertainty. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{bampis_et_al:LIPIcs.APPROX/RANDOM.2024.17,
  author =	{Bampis, Evripidis and Dogeas, Konstantinos and Erlebach, Thomas and Megow, Nicole and Schl\"{o}ter, Jens and Trehan, Amitabh},
  title =	{{Competitive Query Minimization for Stable Matching with One-Sided Uncertainty}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{17:1--17:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.17},
  URN =		{urn:nbn:de:0030-drops-210100},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.17},
  annote =	{Keywords: Matching under Preferences, Stable Marriage, Query-Competitive Algorithms, Uncertainty}
}
  • Refine by Author
  • 10 Even, Guy
  • 5 Medina, Moti
  • 4 Blanc, Guy
  • 4 Kortsarz, Guy
  • 4 Lange, Jane
  • Show More...

  • Refine by Classification
  • 11 Theory of computation → Streaming, sublinear and near linear time algorithms
  • 8 Theory of computation → Design and analysis of algorithms
  • 7 Theory of computation → Graph algorithms analysis
  • 6 Theory of computation → Routing and network design problems
  • 5 Theory of computation → Distributed algorithms
  • Show More...

  • Refine by Keyword
  • 4 Approximation Algorithms
  • 4 Parameterized Complexity
  • 4 Predictions
  • 3 Distributed Algorithms
  • 3 Vertex Cover
  • Show More...

  • Refine by Type
  • 83 document

  • Refine by Publication Year
  • 48 2024
  • 7 2023
  • 5 2020
  • 5 2021
  • 4 2018
  • Show More...

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail