10 Search Results for "Cohen, Ilan Reuven"

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

Authors: Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha

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

Abstract
Online bipartite matching is a classical problem in online algorithms and we know that both the deterministic fractional and randomized integral online matchings achieve the same competitive ratio of 1-1/e. In this work, we study classes of graphs where the online degree is restricted to 2. As expected, one can achieve a competitive ratio of better than 1-1/e in both the deterministic fractional and randomized integral cases, but surprisingly, these ratios are not the same. It was already known that for fractional matching, a 0.75 competitive ratio algorithm is optimal. We show that the folklore Half-Half algorithm achieves a competitive ratio of η ≈ 0.717772… and more surprisingly, show that this is optimal by giving a matching lower-bound. This yields a separation between the two problems: deterministic fractional and randomized integral, showing that it is impossible to obtain a perfect rounding scheme.
Cite as

Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha. Optimal Online Bipartite Matching in Degree-2 Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhangale_et_al:LIPIcs.ISAAC.2025.13,
  author =	{Bhangale, Amey and Chakraborty, Arghya and Harsha, Prahladh},
  title =	{{Optimal Online Bipartite Matching in Degree-2 Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.13},
  URN =		{urn:nbn:de:0030-drops-249216},
  doi =		{10.4230/LIPIcs.ISAAC.2025.13},
  annote =	{Keywords: Online Algorithm, Bipartite matching}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.37
Towards Optimal Distributed Edge Coloring with Fewer Colors

Authors: Manuel Jakob, Yannic Maus, and Florian Schager

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

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

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

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@InProceedings{jakob_et_al:LIPIcs.DISC.2025.37,
  author =	{Jakob, Manuel and Maus, Yannic and Schager, Florian},
  title =	{{Towards Optimal Distributed Edge Coloring with Fewer Colors}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{37:1--37:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.37},
  URN =		{urn:nbn:de:0030-drops-248547},
  doi =		{10.4230/LIPIcs.DISC.2025.37},
  annote =	{Keywords: distributed graph algorithms, edge coloring, LOCAL model}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.48
Improved Streaming Edge Coloring

Authors: Shiri Chechik, Hongyi Chen, and Tianyi Zhang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Given a graph, an edge coloring assigns colors to edges so that no pairs of adjacent edges share the same color. We are interested in edge coloring algorithms under the W-streaming model. In this model, the algorithm does not have enough memory to hold the entire graph, so the edges of the input graph are read from a data stream one by one in an unknown order, and the algorithm needs to print a valid edge coloring in an output stream. The performance of the algorithm is measured by the amount of space and the number of different colors it uses. This streaming edge coloring problem has been studied by several works in recent years. When the input graph contains n vertices and has maximum vertex degree Δ, it is known that in the W-streaming model, an O(Δ²)-edge coloring can be computed deterministically with Õ(n) space [Ansari, Saneian, and Zarrabi-Zadeh, 2022], or an O(Δ^{1.5})-edge coloring can be computed by a Õ(n)-space randomized algorithm [Behnezhad, Saneian, 2024] [Chechik, Mukhtar, Zhang, 2024]. In this paper, we achieve polynomial improvement over previous results. Specifically, we show how to improve the number of colors to Õ(Δ^{4/3+ε}) using space Õ(n) deterministically, for any constant ε > 0. This is the first deterministic result that bypasses the quadratic bound on the number of colors while using near-linear space.
Cite as

Shiri Chechik, Hongyi Chen, and Tianyi Zhang. Improved Streaming Edge Coloring. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chechik_et_al:LIPIcs.ICALP.2025.48,
  author =	{Chechik, Shiri and Chen, Hongyi and Zhang, Tianyi},
  title =	{{Improved Streaming Edge Coloring}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{48:1--48:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.48},
  URN =		{urn:nbn:de:0030-drops-234257},
  doi =		{10.4230/LIPIcs.ICALP.2025.48},
  annote =	{Keywords: edge coloring, streaming}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.98
The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization

Authors: Zhiyi Huang, Chui Shan Lee, Xinkai Shu, and Zhaozi Wang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study the online allocation of divisible items to n agents with additive valuations for p-mean welfare maximization, a problem introduced by Barman, Khan, and Maiti (2022). Our algorithmic and hardness results characterize the optimal competitive ratios for the entire spectrum of -∞ ≤ p ≤ 1. Surprisingly, our improved algorithms for all p ≤ (1)/(log n) are simply the greedy algorithm for the Nash welfare, supplemented with two auxiliary components to ensure all agents have non-zero utilities and to help a small number of agents with low utilities. In this sense, the long arm of Nashian allocation achieves near-optimal competitive ratios not only for Nash welfare but also all the way to egalitarian welfare.
Cite as

Zhiyi Huang, Chui Shan Lee, Xinkai Shu, and Zhaozi Wang. The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 98:1-98:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huang_et_al:LIPIcs.ICALP.2025.98,
  author =	{Huang, Zhiyi and Lee, Chui Shan and Shu, Xinkai and Wang, Zhaozi},
  title =	{{The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{98:1--98:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.98},
  URN =		{urn:nbn:de:0030-drops-234754},
  doi =		{10.4230/LIPIcs.ICALP.2025.98},
  annote =	{Keywords: Online Algorithms, Fair Division, Nash Welfare}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.4
On b-Matching and Fully-Dynamic Maximum k-Edge Coloring

Authors: Antoine El-Hayek, Kathrin Hanauer, and Monika Henzinger

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
Given a graph G that undergoes a sequence of edge insertions and deletions, we study the Maximum k-Edge Coloring problem (MkEC): Having access to k different colors, color as many edges of G as possible such that no two adjacent edges share the same color. While this problem is different from simply maintaining a b-matching with b = k, the two problems are related. However, maximum b-matching can be solved efficiently in the static setting, whereas MkEC is NP-hard and even APX-hard for k ≥ 2. We present new results on both problems: For b-matching, we show a new integrality gap result and we adapt Wajc’s matching sparsification scheme [David Wajc, 2020] for the case where b is a constant. Using these as basis, we give three new algorithms for the dynamic MkEC problem: Our MatchO algorithm builds on the dynamic (2+ε)-approximation algorithm of Bhattacharya, Gupta, and Mohan [Sayan Bhattacharya et al., 2017] for b-matching and achieves a (2+ε)(k+1)/k-approximation in O(poly(log n, ε^-1)) update time against an oblivious adversary. Our MatchA algorithm builds on the dynamic (7+ε)-approximation algorithm by Bhattacharya, Henzinger, and Italiano [Sayan Bhattacharya et al., 2015] for fractional b-matching and achieves a (7+ε)(3k+3)/(3k-1)-approximation in O(poly(log n, ε^-1)) update time against an adaptive adversary. Moreover, our reductions use the dynamic b-matching algorithm as a black box, so any future improvement in the approximation ratio for dynamic b-matching will automatically translate into a better approximation ratio for our algorithms. Finally, we present a greedy algorithm with O(Δ+k) update time, which guarantees a 2.16 approximation factor.
Cite as

Antoine El-Hayek, Kathrin Hanauer, and Monika Henzinger. On b-Matching and Fully-Dynamic Maximum k-Edge Coloring. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{elhayek_et_al:LIPIcs.SAND.2025.4,
  author =	{El-Hayek, Antoine and Hanauer, Kathrin and Henzinger, Monika},
  title =	{{On b-Matching and Fully-Dynamic Maximum k-Edge Coloring}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.4},
  URN =		{urn:nbn:de:0030-drops-230571},
  doi =		{10.4230/LIPIcs.SAND.2025.4},
  annote =	{Keywords: dynamic algorithm, graph algorithm, matching, b-matching, edge coloring}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.35
Unraveling Universally Closest Refinements via Symmetric Density Decomposition and Fisher Market Equilibrium

Authors: T-H. Hubert Chan and Quan Xue

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We investigate the closest distribution refinements problem, which involves a vertex-weighted bipartite graph as input, where the vertex weights on each side sum to 1 and represent a probability distribution. A refinement of one side’s distribution is an edge distribution that corresponds to distributing the weight of each vertex from that side to its incident edges. The objective is to identify a pair of distribution refinements for both sides of the bipartite graph such that the two edge distributions are as close as possible with respect to a specific divergence notion. This problem is a generalization of transportation, in which the special case occurs when the two closest distributions are identical. The problem has recently emerged in the context of composing differentially oblivious mechanisms. Our main result demonstrates that a universal refinement pair exists, which is simultaneously closest under all divergence notions that satisfy the data processing inequality. Since differential obliviousness can be examined using various divergence notions, such a universally closest refinement pair offers a powerful tool in relation to such applications. We discover that this pair can be achieved via locally verifiable optimality conditions. Specifically, we observe that it is equivalent to the following problems, which have been traditionally studied in distinct research communities: (1) hypergraph density decomposition, and (2) symmetric Fisher Market equilibrium. We adopt a symmetric perspective of hypergraph density decomposition, in which hyperedges and nodes play equivalent roles. This symmetric decomposition serves as a tool for deriving precise characterizations of optimal solutions for other problems and enables the application of algorithms from one problem to another. This connection allows existing algorithms for computing or approximating the Fisher market equilibrium to be adapted for all the aforementioned problems. For example, this approach allows the well-known iterative proportional response process to provide approximations for the corresponding problems with multiplicative error in distributed settings, whereas previously, only absolute error had been achieved in these contexts. Our study contributes to the understanding of various problems within a unified framework, which may serve as a foundation for connecting other problems in the future.
Cite as

T-H. Hubert Chan and Quan Xue. Unraveling Universally Closest Refinements via Symmetric Density Decomposition and Fisher Market Equilibrium. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 35:1-35:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chan_et_al:LIPIcs.ITCS.2025.35,
  author =	{Chan, T-H. Hubert and Xue, Quan},
  title =	{{Unraveling Universally Closest Refinements via Symmetric Density Decomposition and Fisher Market Equilibrium}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{35:1--35:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.35},
  URN =		{urn:nbn:de:0030-drops-226633},
  doi =		{10.4230/LIPIcs.ITCS.2025.35},
  annote =	{Keywords: closest distribution refinements, density decomposition, Fisher market equilibrium}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.35
Primal-Dual Schemes for Online Matching in Bounded Degree Graphs

Authors: Ilan Reuven Cohen and Binghui Peng

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We explore various generalizations of the online matching problem in a bipartite graph G as the b-matching problem [Kalyanasundaram and Pruhs, 2000], the allocation problem [Buchbinder et al., 2007], and the AdWords problem [Mehta et al., 2007] in a beyond-worst-case setting. Specifically, we assume that G is a (k, d)-bounded degree graph, introduced by Naor and Wajc [Naor and Wajc, 2018]. Such graphs model natural properties on the degrees of advertisers and queries in the allocation and AdWords problems. While previous work only considers the scenario where k ≥ d, we consider the interesting intermediate regime of k ≤ d and prove a tight competitive ratio as a function of k,d (under the small-bid assumption) of τ(k,d) = 1 - (1-k/d)⋅(1-1/d)^{d - k} for the b-matching and allocation problems. We exploit primal-dual schemes [Buchbinder et al., 2009; Azar et al., 2017] to design and analyze the corresponding tight upper and lower bounds. Finally, we show a separation between the allocation and AdWords problems. We demonstrate that τ(k,d) competitiveness is impossible for the AdWords problem even in (k,d)-bounded degree graphs.
Cite as

Ilan Reuven Cohen and Binghui Peng. Primal-Dual Schemes for Online Matching in Bounded Degree Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cohen_et_al:LIPIcs.ESA.2023.35,
  author =	{Cohen, Ilan Reuven and Peng, Binghui},
  title =	{{Primal-Dual Schemes for Online Matching in Bounded Degree Graphs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.35},
  URN =		{urn:nbn:de:0030-drops-186884},
  doi =		{10.4230/LIPIcs.ESA.2023.35},
  annote =	{Keywords: Online Matching, Primal-dual analysis, bounded-degree graph, the AdWords problem}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.43
A General Framework for Learning-Augmented Online Allocation

Authors: Ilan Reuven Cohen and Debmalya Panigrahi

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Online allocation is a broad class of problems where items arriving online have to be allocated to agents who have a fixed utility/cost for each assigned item so to maximize/minimize some objective. This framework captures a broad range of fundamental problems such as the Santa Claus problem (maximizing minimum utility), Nash welfare maximization (maximizing geometric mean of utilities), makespan minimization (minimizing maximum cost), minimization of 𝓁_p-norms, and so on. We focus on divisible items (i.e., fractional allocations) in this paper. Even for divisible items, these problems are characterized by strong super-constant lower bounds in the classical worst-case online model. In this paper, we study online allocations in the learning-augmented setting, i.e., where the algorithm has access to some additional (machine-learned) information about the problem instance. We introduce a general algorithmic framework for learning-augmented online allocation that produces nearly optimal solutions for this broad range of maximization and minimization objectives using only a single learned parameter for every agent. As corollaries of our general framework, we improve prior results of Lattanzi et al. (SODA 2020) and Li and Xian (ICML 2021) for learning-augmented makespan minimization, and obtain the first learning-augmented nearly-optimal algorithms for the other objectives such as Santa Claus, Nash welfare, 𝓁_p-minimization, etc. We also give tight bounds on the resilience of our algorithms to errors in the learned parameters, and study the learnability of these parameters.
Cite as

Ilan Reuven Cohen and Debmalya Panigrahi. A General Framework for Learning-Augmented Online Allocation. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 43:1-43:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cohen_et_al:LIPIcs.ICALP.2023.43,
  author =	{Cohen, Ilan Reuven and Panigrahi, Debmalya},
  title =	{{A General Framework for Learning-Augmented Online Allocation}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{43:1--43:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.43},
  URN =		{urn:nbn:de:0030-drops-180952},
  doi =		{10.4230/LIPIcs.ICALP.2023.43},
  annote =	{Keywords: Algorithms with predictions, Scheduling algorithms, Online algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.8
Truly Asymptotic Lower Bounds for Online Vector Bin Packing

Authors: János Balogh, Ilan Reuven Cohen, Leah Epstein, and Asaf Levin

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
In this work, we consider online d-dimensional vector bin packing. It is known that no algorithm can have a competitive ratio of o(d/log² d) in the absolute sense, although upper bounds for this problem have always been presented in the asymptotic sense. Since variants of bin packing are traditionally studied with respect to the asymptotic measure, and since the two measures are different, we focus on the asymptotic measure and prove new lower bounds of the asymptotic competitive ratio. The existing lower bounds prior to this work were known to be smaller than 3, even for very large d. Here, we significantly improved on the best known lower bounds of the asymptotic competitive ratio (and as a byproduct, on the absolute competitive ratio) for online vector packing of vectors with d ≥ 3 dimensions, for every dimension d. To obtain these results, we use several different constructions, one of which is an adaptive construction with a lower bound of Ω(√d). Our main result is that the lower bound of Ω(d/log² d) on the competitive ratio holds also in the asymptotic sense. This result holds also against randomized algorithms, and requires a careful adaptation of constructions for online coloring, rather than simple black-box reductions.
Cite as

János Balogh, Ilan Reuven Cohen, Leah Epstein, and Asaf Levin. Truly Asymptotic Lower Bounds for Online Vector Bin Packing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{balogh_et_al:LIPIcs.APPROX/RANDOM.2021.8,
  author =	{Balogh, J\'{a}nos and Cohen, Ilan Reuven and Epstein, Leah and Levin, Asaf},
  title =	{{Truly Asymptotic Lower Bounds for Online Vector Bin Packing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.8},
  URN =		{urn:nbn:de:0030-drops-147013},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.8},
  annote =	{Keywords: Bin packing, online algorithms, approximation algorithms, vector packing}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.10
Dynamic Pricing of Servers on Trees

Authors: Ilan Reuven Cohen, Alon Eden, Amos Fiat, and Łukasz Jeż

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
In this paper we consider the k-server problem where events are generated by selfish agents, known as the selfish k-server problem. In this setting, there is a set of k servers located in some metric space. Selfish agents arrive in an online fashion, each has a request located on some point in the metric space, and seeks to serve his request with the server of minimum distance to the request. If agents choose to serve their request with the nearest server, this mimics the greedy algorithm which has an unbounded competitive ratio. We propose an algorithm that associates a surcharge with each server independently of the agent to arrive (and therefore, yields a truthful online mechanism). An agent chooses to serve his request with the server that minimizes the distance to the request plus the associated surcharge to the server. This paper extends [Ilan Reuven Cohen et al., 2015], which gave an optimal k-competitive dynamic pricing scheme for the selfish k-server problem on the line. We give a k-competitive dynamic pricing algorithm for the selfish k-server problem on tree metric spaces, which matches the optimal online (non truthful) algorithm. We show that an alpha-competitive dynamic pricing scheme exists on the tree if and only if there exists alpha-competitive online algorithm on the tree that is lazy and monotone. Given this characterization, the main technical difficulty is coming up with such an online algorithm.
Cite as

Ilan Reuven Cohen, Alon Eden, Amos Fiat, and Łukasz Jeż. Dynamic Pricing of Servers on Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{cohen_et_al:LIPIcs.APPROX-RANDOM.2019.10,
  author =	{Cohen, Ilan Reuven and Eden, Alon and Fiat, Amos and Je\.{z}, {\L}ukasz},
  title =	{{Dynamic Pricing of Servers on Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{10:1--10:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.10},
  URN =		{urn:nbn:de:0030-drops-112252},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.10},
  annote =	{Keywords: Online algorithms, Online mechanisms, k-server problem, Online pricing}
}
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