Algorithmic discrete mathematics with applications

我对与两个最新发展相关的算法感兴趣。 2002年，Chudnovsky et al.证明了强完美图论，这是自1976年阿佩尔和哈肯1976年证明四色定理以来图论中最大的公开问题。 与最近这一不朽的结果相关的是一个有趣的开放问题：给出一个图表 满足这个定理的条件，有没有一种有效的简单的(所以，不使用椭球方法的复杂数学)方法来寻找最大的集团？ 对于这个问题，我想看看我是否可以在更小的图类上解决这个问题。 2006年，世界了解了电脑围棋程序Crazystone的实力 和Gelly的Mogo。从那时起，计算机围棋领域发生了一场革命，这场革命已经蔓延到计算机科学的许多领域，应用范围广泛，从为多工厂发电系统寻找合适的时间表。在这场革命的背后是蒙特卡洛树搜索，一种新的 在巨大的解空间中执行搜索的随机方法。 对于这个问题，我正在一种比围棋更简单的游戏上试验这些想法。

I am interested in algorithms related to two recent developments. In 2002, Chudnovsky et al. proved the Strong Perfect Graph Theorem, the biggest open problem in graph theory since Appel and Haken's 1976 proof of the Four Color Theorem in 1976. Related to this recent monumental result is an intriguing open problem: given a graph satisfying the conditions of the theorem, is there an efficient simple (so, not using the complicated mathematics of the ellipsoid method) way to find a largest clique ? For this problem, I am seeing if I can solve this problem on a smaller class of graphs. In 2006, the world learned the strength of the computer Go programs Crazystone by Coulom and MoGo by Gelly. Since then, there has been a revolution in computer Go that has spilled into many areas of computer science, with applications as wide ranging as finding suitable schedules for multi-plant power generation systems. Underlying this revolution is Monte Carlo tree search, a new randomized method for performing a search in a huge solution space. For this problem, I am experimenting with these ideas on a simpler game than Go.