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Documents authored by Kantor, Erez

Document
DOI: 10.4230/LIPIcs.ESA.2019.44
Online Disjoint Set Cover Without Prior Knowledge

Authors: Yuval Emek, Adam Goldbraikh, and Erez Kantor

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
The disjoint set cover (DSC) problem is a fundamental combinatorial optimization problem concerned with partitioning the (hyper)edges of a hypergraph into (pairwise disjoint) clusters so that the number of clusters that cover all nodes is maximized. In its online version, the edges arrive one-by-one and should be assigned to clusters in an irrevocable fashion without knowing the future edges. This paper investigates the competitiveness of online DSC algorithms. Specifically, we develop the first (randomized) online DSC algorithm that guarantees a poly-logarithmic (O(log^{2} n)) competitive ratio without prior knowledge of the hypergraph’s minimum degree. On the negative side, we prove that the competitive ratio of any randomized online DSC algorithm must be at least Omega((log n)/(log log n)) (even if the online algorithm does know the minimum degree in advance), thus establishing the first lower bound on the competitive ratio of randomized online DSC algorithms.
Cite as

Yuval Emek, Adam Goldbraikh, and Erez Kantor. Online Disjoint Set Cover Without Prior Knowledge. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 44:1-44:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{emek_et_al:LIPIcs.ESA.2019.44,
  author =	{Emek, Yuval and Goldbraikh, Adam and Kantor, Erez},
  title =	{{Online Disjoint Set Cover Without Prior Knowledge}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{44:1--44:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.44},
  URN =		{urn:nbn:de:0030-drops-111654},
  doi =		{10.4230/LIPIcs.ESA.2019.44},
  annote =	{Keywords: disjoint set cover, online algorithms, competitive analysis, competitiveness with high probability}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.49
Improved Algorithms for Scheduling Unsplittable Flows on Paths

Authors: Hamidreza Jahanjou, Erez Kantor, and Rajmohan Rajaraman

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
In this paper, we investigate offline and online algorithms for Round-UFPP, the problem of minimizing the number of rounds required to schedule a set of unsplittable flows of non-uniform sizes on a given path with non-uniform edge capacities. Round-UFPP is NP-hard and constant-factor approximation algorithms are known under the no bottleneck assumption (NBA), which stipulates that maximum size of a flow is at most the minimum edge capacity. We study Round-UFPP without the NBA, and present improved online and offline algorithms. We first study offline Round-UFPP for a restricted class of instances called alpha-small, where the size of each flow is at most alpha times the capacity of its bottleneck edge, and present an O(log(1/(1 - alpha)))-approximation algorithm. Our main result is an online O(log log cmax)-competitive algorithm for Round-UFPP for general instances, where cmax is the largest edge capacities, improving upon the previous best bound of O(log cmax) due to [16]. Our result leads to an offline O(min(log n, log m, log log cmax))- approximation algorithm and an online O(min(log m, log log cmax))-competitive algorithm for Round-UFPP, where n is the number of flows and m is the number of edges.
Cite as

Hamidreza Jahanjou, Erez Kantor, and Rajmohan Rajaraman. Improved Algorithms for Scheduling Unsplittable Flows on Paths. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 49:1-49:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{jahanjou_et_al:LIPIcs.ISAAC.2017.49,
  author =	{Jahanjou, Hamidreza and Kantor, Erez and Rajaraman, Rajmohan},
  title =	{{Improved Algorithms for Scheduling Unsplittable Flows on Paths}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{49:1--49:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.49},
  URN =		{urn:nbn:de:0030-drops-82292},
  doi =		{10.4230/LIPIcs.ISAAC.2017.49},
  annote =	{Keywords: Approximation algorithms, Online algorithms, Unsplittable flows, Interval coloring, Flow scheduling}
}
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