The Taub Faculty of Computer Science Events and Talks

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, 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 against an adaptive adversary and of 0.8786 against an oblivious adversary (here 0.8786 is the approximation achieved by the random hyperplane algorithm of [Goemans-Williamson J. ACM `95]). Additionally, we present a hardness of approximation of 0.8786 against both types of adversaries, rendering our results (virtually) tight. Based on joint work with Keren Censor-Hillel, Roy Schwartz and Tigran Tonoyan.