English

An improvement of the upper bound for GKS communication game

Computational Complexity 2020-01-14 v1

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(n0.4732)O(n^{0.4732}). Then a protocol with the cost of O(n0.4696)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(n0.4693)O(n^{0.4693}).

Keywords

Cite

@article{arxiv.2001.03924,
  title  = {An improvement of the upper bound for GKS communication game},
  author = {Ivan Petrenko},
  journal= {arXiv preprint arXiv:2001.03924},
  year   = {2020}
}