104 Search Results for "Azar, Yossi"

Volume

LIPIcs, Volume 112

26th Annual European Symposium on Algorithms (ESA 2018)

ESA 2018, August 20-22, 2018, Helsinki, Finland

Editors: Yossi Azar, Hannah Bast, and Grzegorz Herman

Document
DOI: 10.4230/LIPIcs.DISC.2024.27
Sorting in One and Two Rounds Using t-Comparators

Authors: Ran Gelles, Zvi Lotker, and Frederik Mallmann-Trenn

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

Abstract
We examine sorting algorithms for n elements whose basic operation is comparing t elements simultaneously (a t-comparator). We focus on algorithms that use only a single round or two rounds - comparisons performed in the second round depend on the outcomes of the first round comparators. Algorithms with a small number of rounds are well-suited to distributed settings in which communication rounds are costly. We design deterministic and randomized algorithms. In the deterministic case, we show an interesting relation to design theory (namely, to 2-Steiner systems), which yields a single-round optimal algorithm for n = t^{2^k} with any k ≥ 1 and a variety of possible values of t. For some values of t, however, no algorithm can reach the optimal (information-theoretic) bound on the number of comparators. For this case (and any other n and t), we show an algorithm that uses at most three times as many comparators as the theoretical bound. We also design a randomized Las-Vegas two-round sorting algorithm for any n and t. Our algorithm uses an asymptotically optimal number of O(max(n^{3/2}/t²,n/t)) comparators, with high probability, i.e., with probability at least 1-1/n. The analysis of this algorithm involves the gradual unveiling of randomness, using a novel technique which we coin the binary tree of deferred randomness.
Cite as

Ran Gelles, Zvi Lotker, and Frederik Mallmann-Trenn. Sorting in One and Two Rounds Using t-Comparators. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 27:1-27:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gelles_et_al:LIPIcs.DISC.2024.27,
  author =	{Gelles, Ran and Lotker, Zvi and Mallmann-Trenn, Frederik},
  title =	{{Sorting in One and Two Rounds Using t-Comparators}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{27:1--27:20},
  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.2024.27},
  URN =		{urn:nbn:de:0030-drops-212539},
  doi =		{10.4230/LIPIcs.DISC.2024.27},
  annote =	{Keywords: Sorting, Steiner-System, Round Complexity, Deferred Randomness}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.37
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)

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@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
DOI: 10.4230/LIPIcs.ESA.2024.38
Local Optimization Algorithms for Maximum Planar Subgraph

Authors: Gruia Călinescu and Sumedha Uniyal

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

Abstract
Consider the NP-hard problem of, given a simple graph G, to find a planar subgraph of G with the maximum number of edges. This is called the Maximum Planar Subgraph problem and the best known approximation is 4/9 and is obtained by sophisticated Graphic Matroid Parity algorithms. Here we show that applying a local optimization phase to the output of this known algorithm improves this approximation ratio by a small {ε} = 1/747 > 0. This is the first improvement in approximation ratio in more than a quarter century. The analysis relies on a more refined extremal bound on the Lovász cactus number in planar graphs, compared to the earlier (tight) bound of [Gruia Călinescu et al., 1998; Chalermsook et al., 2019]. A second local optimization algorithm achieves a tight ratio of 5/12 for Maximum Planar Subgraph without using Graphic Matroid Parity. We also show that applying a greedy algorithm before this second optimization algorithm improves its ratio to at least 91/216 < 4/9. The motivation for not using Graphic Matroid Parity is that it requires sophisticated algorithms that are not considered practical by previous work. The best previously published [Chalermsook and Schmid, 2017] approximation ratio without Graphic Matroid Parity is 13/33 < 5/12.
Cite as

Gruia Călinescu and Sumedha Uniyal. Local Optimization Algorithms for Maximum Planar Subgraph. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 38:1-38:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{calinescu_et_al:LIPIcs.ESA.2024.38,
  author =	{C\u{a}linescu, Gruia and Uniyal, Sumedha},
  title =	{{Local Optimization Algorithms for Maximum Planar Subgraph}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{38:1--38:18},
  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.2024.38},
  URN =		{urn:nbn:de:0030-drops-211090},
  doi =		{10.4230/LIPIcs.ESA.2024.38},
  annote =	{Keywords: planar graph, maximum subgraph, approximation algorithm, matroid parity, local optimization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.41
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)

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@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
DOI: 10.4230/LIPIcs.ESA.2024.48
Scheduling with Obligatory Tests

Authors: Konstantinos Dogeas, Thomas Erlebach, and Ya-Chun Liang

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

Abstract
Motivated by settings such as medical treatments or aircraft maintenance, we consider a scheduling problem with jobs that consist of two operations, a test and a processing part. The time required to execute the test is known in advance while the time required to execute the processing part becomes known only upon completion of the test. We use competitive analysis to study algorithms for minimizing the sum of completion times for n given jobs on a single machine. As our main result, we prove using a novel analysis technique that the natural 1-SORT algorithm has competitive ratio at most 1.861. For the special case of uniform test times, we show that a simple threshold-based algorithm has competitive ratio at most 1.585. We also prove a lower bound that shows that no deterministic algorithm can be better than √2-competitive even in the case of uniform test times.
Cite as

Konstantinos Dogeas, Thomas Erlebach, and Ya-Chun Liang. Scheduling with Obligatory Tests. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 48:1-48:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dogeas_et_al:LIPIcs.ESA.2024.48,
  author =	{Dogeas, Konstantinos and Erlebach, Thomas and Liang, Ya-Chun},
  title =	{{Scheduling with Obligatory Tests}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{48:1--48:14},
  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.2024.48},
  URN =		{urn:nbn:de:0030-drops-211194},
  doi =		{10.4230/LIPIcs.ESA.2024.48},
  annote =	{Keywords: Competitive ratio, Online algorithm, Scheduling with testing, Sum of completion times}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.79
Giving Some Slack: Shortcuts and Transitive Closure Compressions

Authors: Shimon Kogan and Merav Parter

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

Abstract
We consider the fundamental problems of reachability shortcuts and compression schemes of the transitive closure (TC) of n-vertex directed acyclic graphs (DAGs) G when we are allowed to neglect the distance (or reachability) constraints for an ε fraction of the pairs in the transitive closure of G, denoted by TC(G). Shortcuts with Slack. For a directed graph G = (V,E), a d-reachability shortcut is a set of edges H ⊆ TC(G), whose addition decreases the directed diameter of G to be at most d. We introduce the notion of shortcuts with slack which provide the desired distance bound d for all but a small fraction ε of the vertex pairs in TC(G). For ε ∈ (0,1), a (d,ε)-shortcut H ⊆ TC(G) is a subset of edges with the property that dist_{G ∪ H}(u,v) ≤ d for at least (1-ε) fraction of the (u,v) pairs in TC(G). Our constructions hold for any DAG G and their size bounds are parameterized by the width of the graph G defined by the smallest number of directed paths in G that cover all vertices in G. - For every ε ∈ (0,1] and integer d ≥ 5, every n-vertex DAG G of width {ω} admits a (d,ε)-shortcut of size Õ({ω}²/(ε d)+n). A more delicate construction yields a (3,ε)-shortcut of size Õ({ω}²/(ε d)+n/ε), hence of linear size for {ω} ≤ √n. We show that without a slack (i.e., for ε = 0), graphs with {ω} ≤ √n cannot be shortcut to diameter below n^{1/6} using a linear number of shortcut edges. - There exists an n-vertex DAG G for which any (3,ε = 1/2^{√{log ω}})-shortcut set has Ω({ω}²/2^{√{log ω}}+n) edges. Hence, for d = Õ(1), our constructions are almost optimal. Approximate TC Representations. A key application of our shortcut’s constructions is a (1-ε)-approximate all-successors data structure which given a vertex v, reports a list containing (1-ε) fraction of the successors of v in the graph. We present a Õ({ω}²/ε+n)-space data structure with a near linear (in the output size) query time. Using connections to Error Correcting Codes, we also present a near-matching space lower bound of Ω({ω}²+n) bits (regardless of the query time) for constant ε. This improves upon the state-of-the-art space bounds of O({ω} ⋅ n) for ε = 0 by the prior work of Jagadish [ACM Trans. Database Syst., 1990].
Cite as

Shimon Kogan and Merav Parter. Giving Some Slack: Shortcuts and Transitive Closure Compressions. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 79:1-79:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kogan_et_al:LIPIcs.ESA.2024.79,
  author =	{Kogan, Shimon and Parter, Merav},
  title =	{{Giving Some Slack: Shortcuts and Transitive Closure Compressions}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{79:1--79:15},
  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.2024.79},
  URN =		{urn:nbn:de:0030-drops-211509},
  doi =		{10.4230/LIPIcs.ESA.2024.79},
  annote =	{Keywords: Reachability Shortcuts, Width, DAG}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.95
Competitive Capacitated Online Recoloring

Authors: Rajmohan Rajaraman and Omer Wasim

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

Abstract
In this paper, we revisit the online recoloring problem introduced recently by Azar, Machluf, Patt-Shamir and Touitou [Azar et al., 2022] to investigate algorithmic challenges that arise while scheduling virtual machines or processes in distributed systems and cloud services. In online recoloring, there is a fixed set V of n vertices and an initial coloring c₀: V → [k] for some k ∈ ℤ^{> 0}. Under an online sequence σ of requests where each request is an edge (u_t,v_t), a proper vertex coloring c of the graph G_t induced by requests until time t needs to be maintained for all t; i.e., for any (u,v) ∈ G_t, c(u)≠ c(v). In the distributed systems application, a vertex corresponds to a VM, an edge corresponds to the requirement that the two endpoint VMs be on different clusters, and a coloring is an allocation of VMs to clusters. The objective is to minimize the total weight of vertices recolored for the sequence σ. In [Azar et al., 2022], the authors give competitive algorithms for two polynomially tractable cases - 2-coloring for bipartite G_t and (Δ+1)-coloring for Δ-degree G_t - and lower bounds for the fully dynamic case where G_t can be arbitrary. We obtain the first competitive algorithms for capacitated online recoloring and fully dynamic recoloring, in which there is a bound on the number or weight of vertices in each color. Our first set of results is for 2-recoloring using algorithms that are (1+ε)-resource augmented where ε ∈ (0,1) is an arbitrarily small constant. Our main result is an O(log n)-competitive deterministic algorithm for weighted bipartite graphs, which is asymptotically optimal in light of an Ω(log n) lower bound that holds for an unbounded amount of augmentation. We also present an O(nlog n)-competitive deterministic algorithm for fully dynamic recoloring, which is optimal within an O(log n) factor in light of a Ω(n) lower bound that holds for an unbounded amount of augmentation. Our second set of results is for Δ-recoloring in an (1+ε)-overprovisioned setting where the maximum degree of G_t is bounded by (1-ε)Δ for all t, and each color assigned to at most (1+ε)n/(Δ) vertices, for an arbitrary ε > 0. Our main result is an O(1)-competitive randomized algorithm for Δ = O(√{n/log n}). We also present an O(Δ)-competitive deterministic algorithm for Δ ≤ ε n/2. Both results are asymptotically optimal.
Cite as

Rajmohan Rajaraman and Omer Wasim. Competitive Capacitated Online Recoloring. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 95:1-95:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{rajaraman_et_al:LIPIcs.ESA.2024.95,
  author =	{Rajaraman, Rajmohan and Wasim, Omer},
  title =	{{Competitive Capacitated Online Recoloring}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{95:1--95:17},
  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.2024.95},
  URN =		{urn:nbn:de:0030-drops-211666},
  doi =		{10.4230/LIPIcs.ESA.2024.95},
  annote =	{Keywords: online algorithms, competitive ratio, recoloring, resource augmentation}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.2
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)

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@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
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.10
Improved Online Load Balancing with Known Makespan

Authors: Martin Böhm, Matej Lieskovský, Sören Schmitt, Jiří Sgall, and Rob van Stee

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

Abstract
We break the barrier of 3/2 for the problem of online load balancing with known makespan, also known as bin stretching. In this problem, m identical machines and the optimal makespan are given. The load of a machine is the total size of all the jobs assigned to it and the makespan is the maximum load of all the machines. Jobs arrive online and the goal is to assign each job to a machine while staying within a small factor (the competitive ratio) of the optimal makespan. We present an algorithm that maintains a competitive ratio of 139/93 < 1.495 for sufficiently large values of m, improving the previous bound of 3/2. The value 3/2 represents a natural bound for this problem: as long as the online bins are of size at least 3/2 of the offline bin, all items that fit at least two times in an offline bin have two nice properties. They fit three times in an online bin and a single such item can be packed together with an item of any size in an online bin. These properties are now both lost, which means that putting even one job on a wrong machine can leave some job unassigned at the end. It also makes it harder to determine good thresholds for the item types. This was one of the main technical issues in getting below 3/2. The analysis consists of an intricate mixture of size and weight arguments.
Cite as

Martin Böhm, Matej Lieskovský, Sören Schmitt, Jiří Sgall, and Rob van Stee. Improved Online Load Balancing with Known Makespan. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bohm_et_al:LIPIcs.APPROX/RANDOM.2024.10,
  author =	{B\"{o}hm, Martin and Lieskovsk\'{y}, Matej and Schmitt, S\"{o}ren and Sgall, Ji\v{r}{\'\i} and van Stee, Rob},
  title =	{{Improved Online Load Balancing with Known Makespan}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{10:1--10:21},
  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.2024.10},
  URN =		{urn:nbn:de:0030-drops-210032},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.10},
  annote =	{Keywords: Online algorithms, bin stretching, bin packing}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.12
Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment

Authors: Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, and Seeun William Umboh

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

Abstract
The online joint replenishment problem (JRP) is a fundamental problem in the area of online problems with delay. Over the last decade, several works have studied generalizations of JRP with different cost functions for servicing requests. Most prior works on JRP and its generalizations have focused on the clairvoyant setting. Recently, Touitou [Noam Touitou, 2023] developed a non-clairvoyant framework that provided an O(√{n log n}) upper bound for a wide class of generalized JRP, where n is the number of request types. We advance the study of non-clairvoyant algorithms by providing a simpler, modular framework that matches the competitive ratio established by Touitou for the same class of generalized JRP. Our key insight is to leverage universal algorithms for Set Cover to approximate arbitrary monotone subadditive functions using a simple class of functions termed disjoint. This allows us to reduce the problem to several independent instances of the TCP Acknowledgement problem, for which a simple 2-competitive non-clairvoyant algorithm is known. The modularity of our framework is a major advantage as it allows us to tailor the reduction to specific problems and obtain better competitive ratios. In particular, we obtain tight O(√n)-competitive algorithms for two significant problems: Multi-Level Aggregation and Weighted Symmetric Subadditive Joint Replenishment. We also show that, in contrast, Touitou’s algorithm is Ω(√{n log n})-competitive for both of these problems.
Cite as

Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, and Seeun William Umboh. Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ezra_et_al:LIPIcs.APPROX/RANDOM.2024.12,
  author =	{Ezra, Tomer and Leonardi, Stefano and Paw{\l}owski, Micha{\l} and Russo, Matteo and Umboh, Seeun William},
  title =	{{Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{12:1--12:24},
  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.2024.12},
  URN =		{urn:nbn:de:0030-drops-210050},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.12},
  annote =	{Keywords: Set Cover, Joint Replenishment, TCP-Acknowledgment, Subadditive Function Approximation, Multi-Level Aggregation}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.13
The Average-Value Allocation Problem

Authors: Kshipra Bhawalkar, Zhe Feng, Anupam Gupta, Aranyak Mehta, David Wajc, and Di Wang

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

Abstract
We initiate the study of centralized algorithms for welfare-maximizing allocation of goods to buyers subject to average-value constraints. We show that this problem is NP-hard to approximate beyond a factor of e/(e-1), and provide a 4e/(e-1)-approximate offline algorithm. For the online setting, we show that no non-trivial approximations are achievable under adversarial arrivals. Under i.i.d. arrivals, we present a polytime online algorithm that provides a constant approximation of the optimal (computationally-unbounded) online algorithm. In contrast, we show that no constant approximation of the ex-post optimum is achievable by an online algorithm.
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Kshipra Bhawalkar, Zhe Feng, Anupam Gupta, Aranyak Mehta, David Wajc, and Di Wang. The Average-Value Allocation Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhawalkar_et_al:LIPIcs.APPROX/RANDOM.2024.13,
  author =	{Bhawalkar, Kshipra and Feng, Zhe and Gupta, Anupam and Mehta, Aranyak and Wajc, David and Wang, Di},
  title =	{{The Average-Value Allocation Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{13:1--13:23},
  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.2024.13},
  URN =		{urn:nbn:de:0030-drops-210062},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.13},
  annote =	{Keywords: Resource allocation, return-on-spend constraint, approximation algorithm, online algorithm}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.24
Learning-Augmented Maximum Independent Set

Authors: Vladimir Braverman, Prathamesh Dharangutte, Vihan Shah, and Chen Wang

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

Abstract
We study the Maximum Independent Set (MIS) problem on general graphs within the framework of learning-augmented algorithms. The MIS problem is known to be NP-hard and is also NP-hard to approximate to within a factor of n^(1-δ) for any δ > 0. We show that we can break this barrier in the presence of an oracle obtained through predictions from a machine learning model that answers vertex membership queries for a fixed MIS with probability 1/2+ε. In the first setting we consider, the oracle can be queried once per vertex to know if a vertex belongs to a fixed MIS, and the oracle returns the correct answer with probability 1/2 + ε. Under this setting, we show an algorithm that obtains an Õ((√Δ)/ε)-approximation in O(m) time where Δ is the maximum degree of the graph. In the second setting, we allow multiple queries to the oracle for a vertex, each of which is correct with probability 1/2 + ε. For this setting, we show an O(1)-approximation algorithm using O(n/ε²) total queries and Õ(m) runtime.
Cite as

Vladimir Braverman, Prathamesh Dharangutte, Vihan Shah, and Chen Wang. Learning-Augmented Maximum Independent Set. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{braverman_et_al:LIPIcs.APPROX/RANDOM.2024.24,
  author =	{Braverman, Vladimir and Dharangutte, Prathamesh and Shah, Vihan and Wang, Chen},
  title =	{{Learning-Augmented Maximum Independent Set}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{24:1--24:18},
  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.2024.24},
  URN =		{urn:nbn:de:0030-drops-210179},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.24},
  annote =	{Keywords: Learning-augmented algorithms, maximum independent set, graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.AFT.2024.13
Musketeer: Incentive-Compatible Rebalancing for Payment Channel Networks

Authors: Zeta Avarikioti, Stefan Schmid, and Samarth Tiwari

Published in: LIPIcs, Volume 316, 6th Conference on Advances in Financial Technologies (AFT 2024)

Abstract
In this work, we revisit the severely limited throughput problem of cryptocurrencies and propose a novel rebalancing approach for Payment Channel Networks (PCNs). PCNs are a popular solution for increasing the blockchain throughput, however, their benefit depends on the overall users' liquidity. Rebalancing mechanisms are the state-of-the-art approach to maintaining high liquidity in PCNs. However, existing opt-in rebalancing mechanisms exclude users that may assist in rebalancing for small service fees, leading to suboptimal solutions and under-utilization of the PCNs' bounded liquidity. We introduce the first rebalancing approach for PCNs that includes all users, following a "all for one and one for all" design philosophy that yields optimal throughput. The proposed approach introduces a double-auction rebalancing problem, which we term Musketeer, where users can participate as buyers (paying fees to rebalance) or sellers (charging fees to route transactions). The desired properties tailored to the unique characteristics of PCNs are formally defined, including the novel game-theoretic property of cyclic budget balance that is a stronger variation of strong budget balance. Basic results derived from auction theory, including an impossibility and multiple mechanisms that either achieve all desiderata under a relaxed model or sacrifice one of the properties, are presented. We also propose a novel mechanism that leverages time delays as an additional cost to users. This mechanism is provably truthful, cyclic budget balanced, individually rational and economic efficient but only with respect to liquidity.
Cite as

Zeta Avarikioti, Stefan Schmid, and Samarth Tiwari. Musketeer: Incentive-Compatible Rebalancing for Payment Channel Networks. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{avarikioti_et_al:LIPIcs.AFT.2024.13,
  author =	{Avarikioti, Zeta and Schmid, Stefan and Tiwari, Samarth},
  title =	{{Musketeer: Incentive-Compatible Rebalancing for Payment Channel Networks}},
  booktitle =	{6th Conference on Advances in Financial Technologies (AFT 2024)},
  pages =	{13:1--13:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-345-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{316},
  editor =	{B\"{o}hme, Rainer and Kiffer, Lucianna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2024.13},
  URN =		{urn:nbn:de:0030-drops-209494},
  doi =		{10.4230/LIPIcs.AFT.2024.13},
  annote =	{Keywords: Blockchains, Payment Channel Networks, Rebalancing, Game Theory}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.52
Simultaneously Approximating All 𝓁_p-Norms in Correlation Clustering

Authors: Sami Davies, Benjamin Moseley, and Heather Newman

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
This paper considers correlation clustering on unweighted complete graphs. We give a combinatorial algorithm that returns a single clustering solution that is simultaneously O(1)-approximate for all 𝓁_p-norms of the disagreement vector; in other words, a combinatorial O(1)-approximation of the all-norms objective for correlation clustering. This is the first proof that minimal sacrifice is needed in order to optimize different norms of the disagreement vector. In addition, our algorithm is the first combinatorial approximation algorithm for the 𝓁₂-norm objective, and more generally the first combinatorial algorithm for the 𝓁_p-norm objective when 1 < p < ∞. It is also faster than all previous algorithms that minimize the 𝓁_p-norm of the disagreement vector, with run-time O(n^ω), where O(n^ω) is the time for matrix multiplication on n × n matrices. When the maximum positive degree in the graph is at most Δ, this can be improved to a run-time of O(nΔ² log n).
Cite as

Sami Davies, Benjamin Moseley, and Heather Newman. Simultaneously Approximating All 𝓁_p-Norms in Correlation Clustering. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 52:1-52:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{davies_et_al:LIPIcs.ICALP.2024.52,
  author =	{Davies, Sami and Moseley, Benjamin and Newman, Heather},
  title =	{{Simultaneously Approximating All 𝓁\underlinep-Norms in Correlation Clustering}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{52:1--52:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.52},
  URN =		{urn:nbn:de:0030-drops-201950},
  doi =		{10.4230/LIPIcs.ICALP.2024.52},
  annote =	{Keywords: Approximation algorithms, correlation clustering, all-norms, lp-norms}
}
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