2026-07-23T05:17:58Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14115 2024-03-06T10:53:30Z ddc:004 open_access

Fault Tolerant Max-Cut Censor-Hillel, Keren Marelly, Noa Schwartz, Roy Tonoyan, Tigran fault-tolerance max-cut approximation 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Keren Censor-Hillel and Noa Marelly and Roy Schwartz and Tigran Tonoyan 2021 Is Part Of LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2021.46 urn:nbn:de:0030-drops-141158 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.46 eng https://creativecommons.org/licenses/by/4.0/legalcode