An improvement of the upper bound for GKS communication game

Ivan Petrenko

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arXiv · 2001.03924

An improvement of the upper bound for GKS communication game

Ivan Petrenko

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Abstract

The GKS game was formulated by Justin Gilmer, Michal Koucky, and Michael Saks in their research of the sensitivity conjecture. Mario Szegedy invented a protocol for the game with the cost of $O(n^{0.4732})$. Then a protocol with the cost of $O(n^{0.4696})$ was obtained by DeVon Ingram who used a bipartite matching. We propose a slight improvement of Ingram's method and design a protocol with cost of $O(n^{0.4693})$.

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Ivan Petrenko. 2020-01-12. An improvement of the upper bound for GKS communication game. https://arxiv.org/abs/2001.03924

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