On unique games with negativeweights

Authors:
Peng Cui;Tian Liu;Ke Xu
Affiliations:
School of Information Resource Management, Renmin University of China, Beijing, P.R. China;Ministry of Education, Institute of Software, School of Electronic Engineering and Computer Science, Peking University, Beijing, P.R. China;National Lab of Software Development Environment, Beihang University, Beijing, P.R. China
Venue:
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Year:
2011

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Abstract

In this paper, the authors define Generalized Unique Game Problem (GUGP), where weights of the edges are allowed to be negative. Focuses are made on two special types of GUGP, GUGP-NWA, where the weights of all edges are negative, and GUGP-PWT(ρ), where the total weight of all edges are positive and the negative/positive ratio is at most ρ. The authors investigate the counterpart of the Unique Game Conjecture on GUGP-PWT(ρ). The authors prove Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1), and Unique Game Conjecture holds true on GUGP-PWT(1/2) if the 2-to-1 Conjecture holds true. The authors pose an open problem whether Unique Game Conjecture holds true on GUGPPWT( ρ) with 0