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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2021.46

Fault Tolerant Max-Cut

Authors: Keren Censor-Hillel, Noa Marelly, Roy Schwartz, and Tigran Tonoyan

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract

In this work, we initiate the study of fault tolerant Max-Cut, where given an edge-weighted undirected graph G = (V,E), the goal is to find a cut S ⊆ V that maximizes the total weight of edges that cross S even after an adversary removes k vertices from G. We consider two types of adversaries: an adaptive adversary that sees the outcome of the random coin tosses used by the algorithm, and an oblivious adversary that does not. For any constant number of failures k we present an approximation of (0.878-ε) against an adaptive adversary and of α_{GW}≈ 0.8786 against an oblivious adversary (here α_{GW} is the approximation achieved by the random hyperplane algorithm of [Goemans-Williamson J. ACM `95]). Additionally, we present a hardness of approximation of α_{GW} against both types of adversaries, rendering our results (virtually) tight. The non-linear nature of the fault tolerant objective makes the design and analysis of algorithms harder when compared to the classic Max-Cut. Hence, we employ approaches ranging from multi-objective optimization to LP duality and the ellipsoid algorithm to obtain our results.

Cite as

Keren Censor-Hillel, Noa Marelly, Roy Schwartz, and Tigran Tonoyan. Fault Tolerant Max-Cut. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{censorhillel_et_al:LIPIcs.ICALP.2021.46,
  author =	{Censor-Hillel, Keren and Marelly, Noa and Schwartz, Roy and Tonoyan, Tigran},
  title =	{{Fault Tolerant Max-Cut}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{46:1--46:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.46},
  URN =		{urn:nbn:de:0030-drops-141158},
  doi =		{10.4230/LIPIcs.ICALP.2021.46},
  annote =	{Keywords: fault-tolerance, max-cut, approximation}
}

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Fault Tolerant Max-Cut

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