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Documents authored by Segev, Danny

Document
DOI: 10.4230/LIPIcs.ESA.2017.22
Online Algorithms for Maximum Cardinality Matching with Edge Arrivals

Authors: Niv Buchbinder, Danny Segev, and Yevgeny Tkach

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
In the adversarial edge arrival model for maximum cardinality matching, edges of an unknown graph are revealed one-by-one in arbitrary order, and should be irrevocably accepted or rejected. Here, the goal of an online algorithm is to maximize the number of accepted edges while maintaining a feasible matching at any point in time. For this model, the standard greedy heuristic is 1/2-competitive, and on the other hand, no algorithm that outperforms this ratio is currently known, even for very simple graphs. We present a clean Min-Index framework for devising a family of randomized algorithms, and provide a number of positive and negative results in this context. Among these results, we present a 5/9-competitive algorithm when the underlying graph is a forest, and prove that this ratio is best possible within the Min-Index framework. In addition, we prove a new general upper bound of 2/(3+1/phi^2) ~ 0.5914 on the competitiveness of any algorithm in the edge arrival model. Interestingly, this bound holds even for an easier model in which vertices (along with their adjacent edges) arrive online, and when the underlying graph is a tree of maximum degree at most 3.
Cite as

Niv Buchbinder, Danny Segev, and Yevgeny Tkach. Online Algorithms for Maximum Cardinality Matching with Edge Arrivals. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{buchbinder_et_al:LIPIcs.ESA.2017.22,
  author =	{Buchbinder, Niv and Segev, Danny and Tkach, Yevgeny},
  title =	{{Online Algorithms for Maximum Cardinality Matching with Edge Arrivals}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{22:1--22:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.22},
  URN =		{urn:nbn:de:0030-drops-78206},
  doi =		{10.4230/LIPIcs.ESA.2017.22},
  annote =	{Keywords: Maximum matching, online algorithms, competitive analysis, primal-dual method}
}
Document
DOI: 10.4230/LIPIcs.STACS.2013.389
Improved Bounds for Online Preemptive Matching

Authors: Leah Epstein, Asaf Levin, Danny Segev, and Oren Weimann

Published in: LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

Abstract
When designing a preemptive online algorithm for the maximum matching problem, we wish to maintain a valid matching M while edges of the underlying graph are presented one after the other. When presented with an edge e, the algorithm should decide whether to augment the matching M by adding e (in which case e may be removed later on) or to keep M in its current form without adding e (in which case e is lost for good). The objective is to eventually hold a matching M with maximum weight. The main contribution of this paper is to establish new lower and upper bounds on the competitive ratio achievable by preemptive online algorithms: - We provide a lower bound of 1 + ln 2 \approx 1.693 on the competitive ratio of any randomized algorithm for the maximum cardinality matching problem, thus improving on the currently best known bound of e / (e-1) \approx 1.581 due to Karp, Vazirani, and Vazirani [STOC'90]. - We devise a randomized algorithm that achieves an expected competitive ratio of 5.356 for maximum weight matching. This finding demonstrates the power of randomization in this context, showing how to beat the tight bound of 3 + 2\sqrt{2} \approx 5.828 for deterministic algorithms, obtained by combining the 5.828 upper bound of McGregor [APPROX'05] and the recent 5.828 lower bound of Varadaraja [ICALP'11].
Cite as

Leah Epstein, Asaf Levin, Danny Segev, and Oren Weimann. Improved Bounds for Online Preemptive Matching. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 389-399, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{epstein_et_al:LIPIcs.STACS.2013.389,
  author =	{Epstein, Leah and Levin, Asaf and Segev, Danny and Weimann, Oren},
  title =	{{Improved Bounds for Online Preemptive Matching}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{389--399},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Portier, Natacha and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.389},
  URN =		{urn:nbn:de:0030-drops-39501},
  doi =		{10.4230/LIPIcs.STACS.2013.389},
  annote =	{Keywords: Online algorithms, matching, lower bound}
}
Document
DOI: 10.4230/LIPIcs.STACS.2010.2476
Improved Approximation Guarantees for Weighted Matching in the Semi-Streaming Model

Authors: Leah Epstein, Asaf Levin, Julián Mestre, and Danny Segev

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract
We study the maximum weight matching problem in the semi-streaming model, and improve on the currently best one-pass algorithm due to Zelke (Proc.\ STACS~'08, pages 669--680) by devising a deterministic approach whose performance guarantee is $4.91 + \eps$. In addition, we study {\em preemptive} online algorithms, a sub-class of one-pass algorithms where we are only allowed to maintain a feasible matching in memory at any point in time. All known results prior to Zelke's belong to this sub-class. We provide a lower bound of $4.967$ on the competitive ratio of any such deterministic algorithm, and hence show that future improvements will have to store in memory a set of edges which is not necessarily a feasible matching. We conclude by presenting an empirical study, conducted in order to compare the practical performance of our approach to that of previously suggested algorithms.
Cite as

Leah Epstein, Asaf Levin, Julián Mestre, and Danny Segev. Improved Approximation Guarantees for Weighted Matching in the Semi-Streaming Model. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 347-358, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{epstein_et_al:LIPIcs.STACS.2010.2476,
  author =	{Epstein, Leah and Levin, Asaf and Mestre, Juli\'{a}n and Segev, Danny},
  title =	{{Improved Approximation Guarantees for Weighted Matching in the Semi-Streaming Model}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{347--358},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2476},
  URN =		{urn:nbn:de:0030-drops-24766},
  doi =		{10.4230/LIPIcs.STACS.2010.2476},
  annote =	{Keywords: Approximation guarantees, semi-streaming model, one-pass algorithm}
}
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