On Unique Games with Negative Weights

Peng Cui

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arXiv · 1102.5605

On Unique Games with Negative Weights

Peng Cui

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Abstract

In this paper, the author defines Generalized Unique Game Problem (GUGP), where weights of the edges are allowed to be negative. Two special types of GUGP are illuminated, GUGP-NWA, where the weights of all edges are negative, and GUGP-PWT($\rho$), where the total weight of all edges are positive and the negative-positive ratio is at most $\rho$. The author investigates the counterpart of the Unique Game Conjecture on GUGP-PWT($\rho$). The author shows that Unique Game Conjecture on GUGP-PWT(1) holds true, and Unique Game Conjecture on GUGP-PWT(1/2) holds true, if the 2-to-1 Conjecture holds true. The author poses an open problem whether Unique Game Conjecture holds true on GUGP-PWT($\rho$) with $0<\rho<1$.

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BibTeX RIS

Peng Cui. 2011-02-28. On Unique Games with Negative Weights. https://arxiv.org/abs/1102.5605

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