25 Search Results for "Emek, Yuval"


Document
Information Dissemination via Broadcasts in the Presence of Adversarial Noise

Authors: Klim Efremenko, Gillat Kol, Dmitry Paramonov, Ran Raz, and Raghuvansh R. Saxena

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)


Abstract
We initiate the study of error correcting codes over the multi-party adversarial broadcast channel. Specifically, we consider the classic information dissemination problem where n parties, each holding an input bit, wish to know each other’s input. For this, they communicate in rounds, where, in each round, one designated party sends a bit to all other parties over a channel governed by an adversary that may corrupt a constant fraction of the received communication. We mention that the dissemination problem was studied in the stochastic noise model since the 80’s. While stochastic noise in multi-party channels has received quite a bit of attention, the case of adversarial noise has largely been avoided, as such channels cannot handle more than a 1/n-fraction of errors. Indeed, this many errors allow an adversary to completely corrupt the incoming or outgoing communication for one of the parties and fail the protocol. Curiously, we show that by eliminating these "trivial" attacks, one can get a simple protocol resilient to a constant fraction of errors. Thus, a model that rules out such attacks is both necessary and sufficient to get a resilient protocol. The main shortcoming of our dissemination protocol is its length: it requires Θ(n²) communication rounds whereas n rounds suffice in the absence of noise. Our main result is a matching lower bound of Ω(n²) on the length of any dissemination protocol in our model. Our proof first "gets rid" of the channel noise by converting it to a form of "input noise", showing that a noisy dissemination protocol implies a (noiseless) protocol for a version of the direct sum gap-majority problem. We conclude the proof with a tight lower bound for the latter problem, which may be of independent interest.

Cite as

Klim Efremenko, Gillat Kol, Dmitry Paramonov, Ran Raz, and Raghuvansh R. Saxena. Information Dissemination via Broadcasts in the Presence of Adversarial Noise. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 19:1-19:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{efremenko_et_al:LIPIcs.CCC.2024.19,
  author =	{Efremenko, Klim and Kol, Gillat and Paramonov, Dmitry and Raz, Ran and Saxena, Raghuvansh R.},
  title =	{{Information Dissemination via Broadcasts in the Presence of Adversarial Noise}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{19:1--19:33},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.19},
  URN =		{urn:nbn:de:0030-drops-204159},
  doi =		{10.4230/LIPIcs.CCC.2024.19},
  annote =	{Keywords: Radio Networks, Interactive Coding, Error Correcting Codes}
}
Document
Streaming Matching and Edge Cover in Practice

Authors: S M Ferdous, Alex Pothen, and Mahantesh Halappanavar

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)


Abstract
Graph algorithms with polynomial space and time requirements often become infeasible for massive graphs with billions of edges or more. State-of-the-art approaches therefore employ approximate serial, parallel, and distributed algorithms to tackle these challenges. However, such approaches require storing the entire graph in memory and thus need access to costly computing resources such as clusters and supercomputers. In this paper, we present practical streaming approaches for solving massive graph problems using limited memory for two prototypical graph problems: maximum weighted matching and minimum weighted edge cover. For matching, we conduct a thorough computational study on two of the semi-streaming algorithms including a recent breakthrough result that achieves a 1/(2+ε)-approximation of the weight while using O(n log W /ε) memory (here n is the number of vertices and W is the maximum edge weight), designed by Paz and Schwartzman [SODA, 2017]. Empirically, we show that the semi-streaming algorithms produce matchings whose weight is close to the best 1/2-approximate offline algorithm while requiring less time and an order-of-magnitude less memory. For minimum weighted edge cover, we develop three novel semi-streaming algorithms. Two of these algorithms require a single pass through the input graph, require O(n log n) memory, and provide a 2-approximation guarantee on the objective. We also leverage a relationship between approximate maximum weighted matching and approximate minimum weighted edge cover to develop a two-pass 3/2+ε-approximate algorithm with the memory requirement of Paz and Schwartzman’s semi-streaming matching algorithm. These streaming approaches are compared against the state-of-the-art 3/2-approximate offline algorithm. The semi-streaming matching and the novel edge cover algorithms proposed in this paper can process graphs with several billions of edges in under 30 minutes using 6 GB of memory, which is at least an order of magnitude improvement from the offline (non-streaming) algorithms. For the largest graph, the best alternative offline parallel approximation algorithm (GPA+ROMA) could not finish in three hours even while employing hundreds of processors and 1 TB of memory. We also demonstrate an application of semi-streaming algorithm by computing a matching using linearly bounded memory on intersection graphs derived from three machine learning datasets, while the existing offline algorithms could not complete on one of these datasets since its memory requirement exceeded 1TB.

Cite as

S M Ferdous, Alex Pothen, and Mahantesh Halappanavar. Streaming Matching and Edge Cover in Practice. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{ferdous_et_al:LIPIcs.SEA.2024.12,
  author =	{Ferdous, S M and Pothen, Alex and Halappanavar, Mahantesh},
  title =	{{Streaming Matching and Edge Cover in Practice}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{12:1--12:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.12},
  URN =		{urn:nbn:de:0030-drops-203773},
  doi =		{10.4230/LIPIcs.SEA.2024.12},
  annote =	{Keywords: Matching, Edge Cover, Semi-Streaming Algorithm, Parallel Algorithms, Algorithm Engineering}
}
Document
Track A: Algorithms, Complexity and Games
List Update with Delays or Time Windows

Authors: Yossi Azar, Shahar Lewkowicz, and Danny Vainstein

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


Abstract
We address the problem of List Update, which is considered one of the fundamental problems in online algorithms and competitive analysis. In this context, we are presented with a list of elements and receive requests for these elements over time. Our objective is to fulfill these requests, incurring a cost proportional to their position in the list. Additionally, we can swap any two consecutive elements at a cost of 1. The renowned "Move to Front" algorithm, introduced by Sleator and Tarjan, immediately moves any requested element to the front of the list. They demonstrated that this algorithm achieves a competitive ratio of 2. While this bound is impressive, the actual cost of the algorithm’s solution can be excessively high. For example, if we request the last half of the list, the resulting solution cost becomes quadratic in the list’s length. To address this issue, we consider a more generalized problem called List Update with Time Windows. In this variant, each request arrives with a specific deadline by which it must be served, rather than being served immediately. Moreover, we allow the algorithm to process multiple requests simultaneously, accessing the corresponding elements in a single pass. The cost incurred in this case is determined by the position of the furthest element accessed, leading to a significant reduction in the total solution cost. We introduce this problem to explore lower solution costs, but it necessitates the development of new algorithms. For instance, Move-to-Front fails when handling the simple scenario of requesting the last half of the list with overlapping time windows. In our work, we present a natural O(1) competitive algorithm for this problem. While the algorithm itself is intuitive, its analysis is intricate, requiring the use of a novel potential function. Additionally, we delve into a more general problem called List Update with Delays, where the fixed deadlines are replaced with arbitrary delay functions. In this case, the cost includes not only the access and swapping costs, but also penalties for the delays incurred until the requests are served. This problem encompasses a special case known as the prize collecting version, where a request may go unserved up to a given deadline, resulting in a specified penalty. For this more comprehensive problem, we establish an O(1) competitive algorithm. However, the algorithm for the delay version is more complex, and its analysis involves significantly more intricate considerations.

Cite as

Yossi Azar, Shahar Lewkowicz, and Danny Vainstein. List Update with Delays or Time Windows. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{azar_et_al:LIPIcs.ICALP.2024.15,
  author =	{Azar, Yossi and Lewkowicz, Shahar and Vainstein, Danny},
  title =	{{List Update with Delays or Time Windows}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{15:1--15:20},
  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.2024.15},
  URN =		{urn:nbn:de:0030-drops-201583},
  doi =		{10.4230/LIPIcs.ICALP.2024.15},
  annote =	{Keywords: Online, List Update, Delay, Time Window, Deadline}
}
Document
Track A: Algorithms, Complexity and Games
Bayesian Calibrated Click-Through Auctions

Authors: Junjie Chen, Minming Li, Haifeng Xu, and Song Zuo

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


Abstract
We study information design in click-through auctions, in which the bidders/advertisers bid for winning an opportunity to show their ads but only pay for realized clicks. The payment may or may not happen, and its probability is called the click-through rate (CTR). This auction format is widely used in the industry of online advertising. Bidders have private values, whereas the seller has private information about each bidder’s CTRs. We are interested in the seller’s problem of partially revealing CTR information to maximize revenue. Information design in click-through auctions turns out to be intriguingly different from almost all previous studies in this space since any revealed information about CTRs will never affect bidders' bidding behaviors - they will always bid their true value per click - but only affect the auction’s allocation and payment rule. In some sense, this makes information design effectively a constrained mechanism design problem. Our first result is an FPTAS to compute an approximately optimal mechanism under a constant number of bidders. The design of this algorithm leverages Bayesian bidder values which help to "smooth" the seller’s revenue function and lead to better tractability. The design of this FPTAS is complex and primarily algorithmic. Our second main result pursues the design of "simple" mechanisms that are approximately optimal yet more practical. We primarily focus on the two-bidder situation, which is already notoriously challenging as demonstrated in recent works. When bidders' CTR distribution is symmetric, we develop a simple prior-free signaling scheme, whose construction relies on a parameter termed optimal signal ratio. The constructed scheme provably obtains a good approximation as long as the maximum and minimum of bidders' value density functions do not differ much.

Cite as

Junjie Chen, Minming Li, Haifeng Xu, and Song Zuo. Bayesian Calibrated Click-Through Auctions. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 44:1-44:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{chen_et_al:LIPIcs.ICALP.2024.44,
  author =	{Chen, Junjie and Li, Minming and Xu, Haifeng and Zuo, Song},
  title =	{{Bayesian Calibrated Click-Through Auctions}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{44:1--44:18},
  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.2024.44},
  URN =		{urn:nbn:de:0030-drops-201878},
  doi =		{10.4230/LIPIcs.ICALP.2024.44},
  annote =	{Keywords: information design, ad auctions, online advertising, mechanism design}
}
Document
Improved Deterministic Distributed Maximum Weight Independent Set Approximation in Sparse Graphs

Authors: Yuval Gil

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)


Abstract
We design new deterministic CONGEST approximation algorithms for maximum weight independent set (MWIS) in sparse graphs. As our main results, we obtain new Δ(1+ε)-approximation algorithms as well as algorithms whose approximation ratio depend strictly on α, in graphs with maximum degree Δ and arboricity α. For (deterministic) Δ(1+ε)-approximation, the current state-of-the-art is due to a recent breakthrough by Faour et al. [SODA 2023] that showed an O(log² (Δ W)⋅ log (1/ε)+log ^{*}n)-round algorithm, where W is the largest node-weight (this bound translates to O(log² n⋅log (1/ε)) under the common assumption that W = poly(n)). As for α-dependent approximations, a deterministic CONGEST (8(1+ε)⋅α)-approximation algorithm with runtime O(log³ n⋅log (1/ε)) can be derived by combining the aforementioned algorithm of Faour et al. with a method presented by Kawarabayashi et al. [DISC 2020]. As our main results, we show the following. - A deterministic CONGEST algorithm that computes an α^{1+τ}-approximation for MWIS in O(log nlog α) rounds for any constant τ > 0. To the best of our knowledge, this is the fastest runtime of any deterministic non-trivial approximation algorithm for MWIS to date. Furthermore, for the large class of graphs where α = Δ^{1-Θ(1)}, it implies a deterministic Δ^{1-Θ(1)}-approximation algorithm with a runtime of O(log nlog α) which improves upon the result of Faour et al. in both approximation ratio (by a Δ^{Θ(1)} factor) and runtime (by an O(log n/log α) factor). - A deterministic CONGEST algorithm that computes an O(α)-approximation for MWIS in O(α^{τ}log n) rounds for any (desirably small) constant τ > 0. This improves the runtime of the best known deterministic O(α)-approximation algorithm in the case that α = O(polylog n). This also leads to a deterministic Δ(1+ε)-approximation algorithm with a runtime of O(α^{τ}log nlog (1/ε)) which improves upon the runtime of Faour et al. in the case that α = O(polylog n). - A deterministic CONGEST algorithm that computes a (⌊(2+ε)α⌋)-approximation for MWIS in O(αlog n) rounds. This improves upon the best known α-dependent approximation ratio by a constant factor. - A deterministic CONGEST algorithm that computes a 2d²-approximation for MWIS in time O(d²+log ^{*}n) in a directed graph with out-degree at most d. The dependency on n is (asymptotically) optimal due to a lower bound by Czygrinow et al. [DISC 2008] and Lenzen and Wattenhofer [DISC 2008]. We note that a key ingredient to all of our algorithms is a novel deterministic method that computes a high-weight subset of nodes whose induced subgraph is sparse.

Cite as

Yuval Gil. Improved Deterministic Distributed Maximum Weight Independent Set Approximation in Sparse Graphs. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{gil:LIPIcs.OPODIS.2023.16,
  author =	{Gil, Yuval},
  title =	{{Improved Deterministic Distributed Maximum Weight Independent Set Approximation in Sparse Graphs}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{16:1--16:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.16},
  URN =		{urn:nbn:de:0030-drops-195067},
  doi =		{10.4230/LIPIcs.OPODIS.2023.16},
  annote =	{Keywords: Approximation algorithms, Sparse graphs, The CONGEST model}
}
Document
On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions

Authors: Anne Condon, Yuval Emek, and Noga Harlev

Published in: LIPIcs, Volume 276, 29th International Conference on DNA Computing and Molecular Programming (DNA 29) (2023)


Abstract
This paper studies the (discrete) chemical reaction network (CRN) computational model that emerged in the last two decades as an abstraction for molecular programming. The correctness of CRN protocols is typically established under one of two possible schedulers that determine how the execution advances: (1) a stochastic scheduler that obeys the (continuous time) Markov process dictated by the standard model of stochastic chemical kinetics; or (2) an adversarial scheduler whose only commitment is to maintain a certain fairness condition. The latter scheduler is justified by the fact that the former one crucially assumes "idealized conditions" that more often than not, do not hold in real wet-lab experiments. However, when it comes to analyzing the runtime of CRN protocols, the existing literature focuses strictly on the stochastic scheduler, thus raising the research question that drives this work: Is there a meaningful way to quantify the runtime of CRNs without the idealized conditions assumption? The main conceptual contribution of the current paper is to answer this question in the affirmative, formulating a new runtime measure for CRN protocols that does not rely on idealized conditions. This runtime measure is based on an adapted (weaker) fairness condition as well as a novel scheme that enables partitioning the execution into short rounds and charging the runtime for each round individually (inspired by definitions for the runtime of asynchronous distributed algorithms). Following that, we turn to investigate various fundamental computational tasks and establish (often tight) bounds on the runtime of the corresponding CRN protocols operating under the adversarial scheduler. This includes an almost complete chart of the runtime complexity landscape of predicate decidability tasks.

Cite as

Anne Condon, Yuval Emek, and Noga Harlev. On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{condon_et_al:LIPIcs.DNA.29.3,
  author =	{Condon, Anne and Emek, Yuval and Harlev, Noga},
  title =	{{On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions}},
  booktitle =	{29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
  pages =	{3:1--3:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-297-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{276},
  editor =	{Chen, Ho-Lin and Evans, Constantine G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.29.3},
  URN =		{urn:nbn:de:0030-drops-187861},
  doi =		{10.4230/LIPIcs.DNA.29.3},
  annote =	{Keywords: chemical reaction networks, adversarial runtime, weak fairness, predicate decidability}
}
Document
Online Algorithms with Randomly Infused Advice

Authors: Yuval Emek, Yuval Gil, Maciej Pacut, and Stefan Schmid

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


Abstract
We introduce a novel method for the rigorous quantitative evaluation of online algorithms that relaxes the "radical worst-case" perspective of classic competitive analysis. In contrast to prior work, our method, referred to as randomly infused advice (RIA), does not make any assumptions about the input sequence and does not rely on the development of designated online algorithms. Rather, it can be applied to existing online randomized algorithms, introducing a means to evaluate their performance in scenarios that lie outside the radical worst-case regime. More concretely, an online algorithm ALG with RIA benefits from pieces of advice generated by an omniscient but not entirely reliable oracle. The crux of the new method is that the advice is provided to ALG by writing it into the buffer ℬ from which ALG normally reads its random bits, hence allowing us to augment it through a very simple and non-intrusive interface. The (un)reliability of the oracle is captured via a parameter 0 ≤ α ≤ 1 that determines the probability (per round) that the advice is successfully infused by the oracle; if the advice is not infused, which occurs with probability 1 - α, then the buffer ℬ contains fresh random bits (as in the classic online setting). The applicability of the new RIA method is demonstrated by applying it to three extensively studied online problems: paging, uniform metrical task systems, and online set cover. For these problems, we establish new upper bounds on the competitive ratio of classic online algorithms that improve as the infusion parameter α increases. These are complemented with (often tight) lower bounds on the competitive ratio of online algorithms with RIA for the three problems.

Cite as

Yuval Emek, Yuval Gil, Maciej Pacut, and Stefan Schmid. Online Algorithms with Randomly Infused Advice. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{emek_et_al:LIPIcs.ESA.2023.44,
  author =	{Emek, Yuval and Gil, Yuval and Pacut, Maciej and Schmid, Stefan},
  title =	{{Online Algorithms with Randomly Infused Advice}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{44:1--44:19},
  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.2023.44},
  URN =		{urn:nbn:de:0030-drops-186970},
  doi =		{10.4230/LIPIcs.ESA.2023.44},
  annote =	{Keywords: Online algorithms, competitive analysis, advice}
}
Document
Design of Self-Stabilizing Approximation Algorithms via a Primal-Dual Approach

Authors: Yuval Emek, Yuval Gil, and Noga Harlev

Published in: LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)


Abstract
Self-stabilization is an important concept in the realm of fault-tolerant distributed computing. In this paper, we propose a new approach that relies on the properties of linear programming duality to obtain self-stabilizing approximation algorithms for distributed graph optimization problems. The power of this new approach is demonstrated by the following results: - A self-stabilizing 2(1+ε)-approximation algorithm for minimum weight vertex cover that converges in O(logΔ /(εlog log Δ)) synchronous rounds. - A self-stabilizing Δ-approximation algorithm for maximum weight independent set that converges in O(Δ+log^* n) synchronous rounds. - A self-stabilizing ((2ρ+1)(1+ε))-approximation algorithm for minimum weight dominating set in ρ-arboricity graphs that converges in O((logΔ)/ε) synchronous rounds. In all of the above, Δ denotes the maximum degree. Our technique improves upon previous results in terms of time complexity while incurring only an additive O(log n) overhead to the message size. In addition, to the best of our knowledge, we provide the first self-stabilizing algorithms for the weighted versions of minimum vertex cover and maximum independent set.

Cite as

Yuval Emek, Yuval Gil, and Noga Harlev. Design of Self-Stabilizing Approximation Algorithms via a Primal-Dual Approach. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 27:1-27:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{emek_et_al:LIPIcs.OPODIS.2022.27,
  author =	{Emek, Yuval and Gil, Yuval and Harlev, Noga},
  title =	{{Design of Self-Stabilizing Approximation Algorithms via a Primal-Dual Approach}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{27:1--27:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.27},
  URN =		{urn:nbn:de:0030-drops-176474},
  doi =		{10.4230/LIPIcs.OPODIS.2022.27},
  annote =	{Keywords: self-stabilization, approximation algorithms, primal-dual}
}
Document
Beeping Shortest Paths via Hypergraph Bipartite Decomposition

Authors: Fabien Dufoulon, Yuval Emek, and Ran Gelles

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)


Abstract
Constructing a shortest path between two network nodes is a fundamental task in distributed computing. This work develops schemes for the construction of shortest paths in randomized beeping networks between a predetermined source node and an arbitrary set of destination nodes. Our first scheme constructs a (single) shortest path to an arbitrary destination in O(D log log n + log³ n) rounds with high probability. Our second scheme constructs multiple shortest paths, one per each destination, in O(D log² n + log³ n) rounds with high probability. Our schemes are based on a reduction of the above shortest path construction tasks to a decomposition of hypergraphs into bipartite hypergraphs: We develop a beeping procedure that partitions the hyperedge set of a hypergraph H = (V_H, E_H) into k = Θ (log² n) disjoint subsets F₁ ∪ ⋯ ∪ F_k = E_H such that the (sub-)hypergraph (V_H, F_i) is bipartite in the sense that there exists a vertex subset U ⊆ V such that |U ∩ e| = 1 for every e ∈ F_i. This procedure turns out to be instrumental in speeding up shortest path constructions under the beeping model.

Cite as

Fabien Dufoulon, Yuval Emek, and Ran Gelles. Beeping Shortest Paths via Hypergraph Bipartite Decomposition. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 45:1-45:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{dufoulon_et_al:LIPIcs.ITCS.2023.45,
  author =	{Dufoulon, Fabien and Emek, Yuval and Gelles, Ran},
  title =	{{Beeping Shortest Paths via Hypergraph Bipartite Decomposition}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{45:1--45:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.45},
  URN =		{urn:nbn:de:0030-drops-175485},
  doi =		{10.4230/LIPIcs.ITCS.2023.45},
  annote =	{Keywords: Beeping Networks, Shortest Paths, Hypergraph Bipartite Decomposition}
}
Document
Locally Restricted Proof Labeling Schemes

Authors: Yuval Emek, Yuval Gil, and Shay Kutten

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)


Abstract
Introduced by Korman, Kutten, and Peleg (PODC 2005), a proof labeling scheme (PLS) is a distributed verification system dedicated to evaluating if a given configured graph satisfies a certain property. It involves a centralized prover, whose role is to provide proof that a given configured graph is a yes-instance by means of assigning labels to the nodes, and a distributed verifier, whose role is to verify the validity of the given proof via local access to the assigned labels. In this paper, we introduce the notion of a locally restricted PLS in which the prover’s power is restricted to that of a LOCAL algorithm with a polylogarithmic number of rounds. To circumvent inherent impossibilities of PLSs in the locally restricted setting, we turn to models that relax the correctness requirements by allowing the verifier to accept some no-instances as long as they are not "too far" from satisfying the property in question. To this end, we evaluate (1) distributed graph optimization problems (OptDGPs) based on the notion of an approximate proof labeling scheme (APLS) (analogous to the type of relaxation used in sequential approximation algorithms); and (2) configured graph families (CGFs) based on the notion of a testing proof labeling schemes (TPLS) (analogous to the type of relaxation used in property testing algorithms). The main contribution of the paper comes in the form of two generic compilers, one for OptDGPs and one for CGFs: given a black-box access to an APLS (resp., PLS) for a large class of OptDGPs (resp., CGFs), the compiler produces a locally restricted APLS (resp., TPLS) for the same problem, while losing at most a (1 + ε) factor in the scheme’s relaxation guarantee. An appealing feature of the two compilers is that they only require a logarithmic additive label size overhead.

Cite as

Yuval Emek, Yuval Gil, and Shay Kutten. Locally Restricted Proof Labeling Schemes. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{emek_et_al:LIPIcs.DISC.2022.20,
  author =	{Emek, Yuval and Gil, Yuval and Kutten, Shay},
  title =	{{Locally Restricted Proof Labeling Schemes}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{20:1--20:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.20},
  URN =		{urn:nbn:de:0030-drops-172111},
  doi =		{10.4230/LIPIcs.DISC.2022.20},
  annote =	{Keywords: proof labeling schemes, generic compilers, SLOCAL algorithms}
}
Document
Online Paging with a Vanishing Regret

Authors: Yuval Emek, Shay Kutten, and Yangguang Shi

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)


Abstract
This paper considers a variant of the online paging problem, where the online algorithm has access to multiple predictors, each producing a sequence of predictions for the page arrival times. The predictors may have occasional prediction errors and it is assumed that at least one of them makes a sublinear number of prediction errors in total. Our main result states that this assumption suffices for the design of a randomized online algorithm whose time-average regret with respect to the optimal offline algorithm tends to zero as the time tends to infinity. This holds (with different regret bounds) for both the full information access model, where in each round, the online algorithm gets the predictions of all predictors, and the bandit access model, where in each round, the online algorithm queries a single predictor. While online algorithms that exploit inaccurate predictions have been a topic of growing interest in the last few years, to the best of our knowledge, this is the first paper that studies this topic in the context of multiple predictors for an online problem with unbounded request sequences. Moreover, to the best of our knowledge, this is also the first paper that aims for (and achieves) online algorithms with a vanishing regret for a classic online problem under reasonable assumptions.

Cite as

Yuval Emek, Shay Kutten, and Yangguang Shi. Online Paging with a Vanishing Regret. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 67:1-67:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{emek_et_al:LIPIcs.ITCS.2021.67,
  author =	{Emek, Yuval and Kutten, Shay and Shi, Yangguang},
  title =	{{Online Paging with a Vanishing Regret}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{67:1--67:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.67},
  URN =		{urn:nbn:de:0030-drops-136065},
  doi =		{10.4230/LIPIcs.ITCS.2021.67},
  annote =	{Keywords: online paging, inaccurate predictions, multiple predictors, vanishing regret, full information vs. bandit access}
}
Document
Communication Efficient Self-Stabilizing Leader Election

Authors: Xavier Défago, Yuval Emek, Shay Kutten, Toshimitsu Masuzawa, and Yasumasa Tamura

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)


Abstract
This paper presents a randomized self-stabilizing algorithm that elects a leader r in a general n-node undirected graph and constructs a spanning tree T rooted at r. The algorithm works under the synchronous message passing network model, assuming that the nodes know a linear upper bound on n and that each edge has a unique ID known to both its endpoints (or, alternatively, assuming the KT₁ model). The highlight of this algorithm is its superior communication efficiency: It is guaranteed to send a total of Õ (n) messages, each of constant size, till stabilization, while stabilizing in Õ (n) rounds, in expectation and with high probability. After stabilization, the algorithm sends at most one constant size message per round while communicating only over the (n - 1) edges of T. In all these aspects, the communication overhead of the new algorithm is far smaller than that of the existing (mostly deterministic) self-stabilizing leader election algorithms. The algorithm is relatively simple and relies mostly on known modules that are common in the fault free leader election literature; these modules are enhanced in various subtle ways in order to assemble them into a communication efficient self-stabilizing algorithm.

Cite as

Xavier Défago, Yuval Emek, Shay Kutten, Toshimitsu Masuzawa, and Yasumasa Tamura. Communication Efficient Self-Stabilizing Leader Election. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{defago_et_al:LIPIcs.DISC.2020.11,
  author =	{D\'{e}fago, Xavier and Emek, Yuval and Kutten, Shay and Masuzawa, Toshimitsu and Tamura, Yasumasa},
  title =	{{Communication Efficient Self-Stabilizing Leader Election}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.11},
  URN =		{urn:nbn:de:0030-drops-130892},
  doi =		{10.4230/LIPIcs.DISC.2020.11},
  annote =	{Keywords: self-stabilization, leader election, communication overhead}
}
Document
Twenty-Two New Approximate Proof Labeling Schemes

Authors: Yuval Emek and Yuval Gil

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)


Abstract
Introduced by Korman, Kutten, and Peleg (Distributed Computing 2005), a proof labeling scheme (PLS) is a system dedicated to verifying that a given configuration graph satisfies a certain property. It is composed of a centralized prover, whose role is to generate a proof for yes-instances in the form of an assignment of labels to the nodes, and a distributed verifier, whose role is to verify the validity of the proof by local means and accept it if and only if the property is satisfied. To overcome lower bounds on the label size of PLSs for certain graph properties, Censor-Hillel, Paz, and Perry (SIROCCO 2017) introduced the notion of an approximate proof labeling scheme (APLS) that allows the verifier to accept also some no-instances as long as they are not "too far" from satisfying the property. The goal of the current paper is to advance our understanding of the power and limitations of APLSs. To this end, we formulate the notion of APLSs in terms of distributed graph optimization problems (OptDGPs) and develop two generic methods for the design of APLSs. These methods are then applied to various classic OptDGPs, obtaining twenty-two new APLSs. An appealing characteristic of our APLSs is that they are all sequentially efficient in the sense that both the prover and the verifier are required to run in (sequential) polynomial time. On the negative side, we establish "combinatorial" lower bounds on the label size for some of the aforementioned OptDGPs that demonstrate the optimality of our corresponding APLSs. For other OptDGPs, we establish conditional lower bounds that exploit the sequential efficiency of the verifier alone (under the assumption that NP ≠ co-NP) or that of both the verifier and the prover (under the assumption that P ≠ NP, with and without the unique games conjecture).

Cite as

Yuval Emek and Yuval Gil. Twenty-Two New Approximate Proof Labeling Schemes. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{emek_et_al:LIPIcs.DISC.2020.20,
  author =	{Emek, Yuval and Gil, Yuval},
  title =	{{Twenty-Two New Approximate Proof Labeling Schemes}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.20},
  URN =		{urn:nbn:de:0030-drops-130983},
  doi =		{10.4230/LIPIcs.DISC.2020.20},
  annote =	{Keywords: proof labeling schemes, distributed graph problems, approximation algorithms}
}
Document
Towards Distributed Two-Stage Stochastic Optimization

Authors: Yuval Emek, Noga Harlev, and Taisuke Izumi

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)


Abstract
The weighted vertex cover problem is concerned with selecting a subset of the vertices that covers a target set of edges with the objective of minimizing the total cost of the selected vertices. We consider a variant of this classic combinatorial optimization problem where the target edge set is not fully known; rather, it is characterized by a probability distribution. Adhering to the model of two-stage stochastic optimization, the execution is divided into two stages so that in the first stage, the decision maker selects some of the vertices based on the probabilistic forecast of the target edge set. Then, in the second stage, the edges in the target set are revealed and in order to cover them, the decision maker can augment the vertex subset selected in the first stage with additional vertices. However, in the second stage, the vertex cost increases by some inflation factor, so the second stage selection becomes more expensive. The current paper studies the two-stage stochastic vertex cover problem in the realm of distributed graph algorithms, where the decision making process (in both stages) is distributed among the vertices of the graph. By combining the stochastic optimization toolbox with recent advances in distributed algorithms for weighted vertex cover, we develop an algorithm that runs in time O(log (Δ) / ε), sends O(m) messages in total, and guarantees to approximate the optimal solution within a (3 + ε)-ratio, where m is the number of edges in the graph, Δ is its maximum degree, and 0 < ε < 1 is a performance parameter.

Cite as

Yuval Emek, Noga Harlev, and Taisuke Izumi. Towards Distributed Two-Stage Stochastic Optimization. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{emek_et_al:LIPIcs.OPODIS.2019.32,
  author =	{Emek, Yuval and Harlev, Noga and Izumi, Taisuke},
  title =	{{Towards Distributed Two-Stage Stochastic Optimization}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.32},
  URN =		{urn:nbn:de:0030-drops-118187},
  doi =		{10.4230/LIPIcs.OPODIS.2019.32},
  annote =	{Keywords: weighted vertex cover, distributed graph algorithms, two-stage stochastic optimization, primal-dual}
}
Document
Low Diameter Graph Decompositions by Approximate Distance Computation

Authors: Ruben Becker, Yuval Emek, and Christoph Lenzen

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)


Abstract
In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the probability that an edge is cut by the decomposition scales linearly with the length of the edge. There is a large body of literature on low diameter graph decomposition with small edge cutting probabilities, with all existing techniques heavily building on single source shortest paths (SSSP) computations. Unfortunately, in many theoretical models for large-scale computations, the SSSP task constitutes a complexity bottleneck. Therefore, it is desirable to replace exact SSSP computations with approximate ones. However this imposes a fundamental challenge since the existing constructions of low diameter graph decomposition with small edge cutting probabilities inherently rely on the subtractive form of the triangle inequality, which fails to hold under distance approximation. The current paper overcomes this obstacle by developing a technique termed blurry ball growing. By combining this technique with a clever algorithmic idea of Miller et al. (SPAA 2013), we obtain a construction of low diameter decompositions with small edge cutting probabilities which replaces exact SSSP computations by (a small number of) approximate ones. The utility of our approach is showcased by deriving efficient algorithms that work in the CONGEST, PRAM, and semi-streaming models of computation. As an application, we obtain metric tree embedding algorithms in the vein of Bartal (FOCS 1996) whose computational complexities in these models are optimal up to polylogarithmic factors. Our embeddings have the additional useful property that the tree can be mapped back to the original graph such that each edge is "used" only logaritmically many times, which is of interest for capacitated problems and simulating CONGEST algorithms on the tree into which the graph is embedded.

Cite as

Ruben Becker, Yuval Emek, and Christoph Lenzen. Low Diameter Graph Decompositions by Approximate Distance Computation. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 50:1-50:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{becker_et_al:LIPIcs.ITCS.2020.50,
  author =	{Becker, Ruben and Emek, Yuval and Lenzen, Christoph},
  title =	{{Low Diameter Graph Decompositions by Approximate Distance Computation}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{50:1--50:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.50},
  URN =		{urn:nbn:de:0030-drops-117355},
  doi =		{10.4230/LIPIcs.ITCS.2020.50},
  annote =	{Keywords: graph decompositions, metric tree embeddings, distributed graph algorithms, parallel graph algorithms, (semi-)streaming graph algorithms}
}
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