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Fault Tolerant Max-Cut

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

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Author Details

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

Funding

This project has received funding from the European Research Council (ERC), under the European Unions Horizon 2020 research and innovation programme under grant agreement No 755839, and from Israel Science Foundation (ISF), under grant No 1336/16.

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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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