Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players

Games on the Sperner Triangle

We create a new two-player game on the Sperner Triangle based on Sperner's lemma. Our game has simple rules and several desirable properties. First, the game is always certain to have a winner. Second, like many other interesting games such as Hex and Geography, we prove that deciding whether one can win our game is a PSPACE-complete problem. Third, there is an elegant balance in the game such that neither the first nor the second player always has a decisive advantage. We provide a web-based version of the game, playable at: http://cs-people.bu.edu/paithan/spernerGame/ . In addition we propos…

分布式三角形检测在少数轮次中是困难的

Distributed Triangle Detection is Hard in Few Rounds

针对分布式三角形检测问题，本文提出一种结合多趟图流下界与点对点通信特性的新信息论论证方法，证明了任何分布式协议均需 $Ω(\log\log{n})$ 轮通信。

Three-player entangled XOR games are NP-hard to approximate

We show that for any eps>0 the problem of finding a factor (2-eps) approximation to the entangled value of a three-player XOR game is NP-hard. Equivalently, the problem of approximating the largest possible quantum violation of a tripartite Bell correlation inequality to within any multiplicative constant is NP-hard. These results are the first constant-factor hardness of approximation results for entangled games or quantum violations of Bell inequalities shown under the sole assumption that P \neq NP. They can be thought of as an extension of Hastad's optimal hardness of approximation results…