M.Sc Thesis


M.Sc StudentMarelly Noa
SubjectFault Tolerant Max-Cut
DepartmentDepartment of Computer Science
Supervisors ASSOCIATE PROF. Keren Censor-Hillel
ASSOCIATE PROF. Roy Schwartz
Full Thesis textFull thesis text - English Version


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, 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 αGW (approximately 0.8786) against an oblivious adversary (here αGW is the approximation achieved by the random hyperplane algorithm of [Goemans-Williamson J. ACM `95]).

Additionally, we present a hardness of approximation of αGW 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.