3 Search Results for "Kantor, Erez"

Document
DOI: 10.4230/LIPIcs.ESA.2024.41
Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing

Authors: Chandra Chekuri and Rhea Jain

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

Abstract
We consider two-cost network design models in which edges of the input graph have an associated cost and length. We build upon recent advances in hop-constrained oblivious routing to obtain two sets of results. We address multicommodity buy-at-bulk network design in the nonuniform setting. Existing poly-logarithmic approximations are based on the junction tree approach [Chekuri et al., 2010; Guy Kortsarz and Zeev Nutov, 2011]. We obtain a new polylogarithmic approximation via a natural LP relaxation. This establishes an upper bound on its integrality gap and affirmatively answers an open question raised in [Chekuri et al., 2010]. The rounding is based on recent results in hop-constrained oblivious routing [Ghaffari et al., 2021], and this technique yields a polylogarithmic approximation in more general settings such as set connectivity. Our algorithm for buy-at-bulk network design is based on an LP-based reduction to h-hop constrained network design for which we obtain LP-based bicriteria approximation algorithms. We also consider a fault-tolerant version of h-hop constrained network design where one wants to design a low-cost network to guarantee short paths between a given set of source-sink pairs even when k-1 edges can fail. This model has been considered in network design [Luis Gouveia and Markus Leitner, 2017; Gouveia et al., 2018; Arslan et al., 2020] but no approximation algorithms were known. We obtain polylogarithmic bicriteria approximation algorithms for the single-source setting for any fixed k. We build upon the single-source algorithm and the junction-tree approach to obtain an approximation algorithm for the multicommodity setting when at most one edge can fail.
Cite as

Chandra Chekuri and Rhea Jain. Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 41:1-41:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chekuri_et_al:LIPIcs.ESA.2024.41,
  author =	{Chekuri, Chandra and Jain, Rhea},
  title =	{{Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{41:1--41:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.41},
  URN =		{urn:nbn:de:0030-drops-211124},
  doi =		{10.4230/LIPIcs.ESA.2024.41},
  annote =	{Keywords: Buy-at-bulk, Hop-constrained network design, LP integrality gap, Fault-tolerant network design}
}
Document
DOI: 10.4230/LIPIcs.ESA.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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