Fault Tolerant Max-Cut

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



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Keren Censor-Hillel
  • Department of Computer Science, Technion, Haifa, Israel
Noa Marelly
  • Department of Computer Science, Technion, Haifa, Israel
Roy Schwartz
  • Department of Computer Science, Technion, Haifa, Israel
Tigran Tonoyan
  • Department of Computer Science, Technion, Haifa, Israel

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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)
https://doi.org/10.4230/LIPIcs.ICALP.2021.46

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Approximation algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • fault-tolerance
  • max-cut
  • approximation

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