利用随机Warnsdorff规则计算Knight's Tours
Counting Knight's Tours through the Randomized Warnsdorff Rule
摘要：
我们给出了一个估计的数量几何不同的开放旅游$\G$的一个骑士在棋盘上。我们使用Warnsdorff规则的随机化来实现回溯方案中的重要性抽样，根据所提出的“大多数解决方案在大多数时间内遵循Warnsdorff规则”的原则来校正原始规则的观察到的偏差。经过一些实验，以测试这一原则，并校准一个参数，解释为距离的一般解决方案从一个Warnsdorff解决方案，我们推测，$\G=1.22\times 10^{15}$。
英文摘要：
We give an estimate of the number of geometrically distinct open tours $\G$ for a knight on a chessboard. We use a randomization of Warnsdorff rule to implement importance sampling in a backtracking scheme, correcting the observed bias of the original rule, according to the proposed principle that ``most solutions follow Warnsdorff rule most of the time''. After some experiments in order to test this principle, and to calibrate a parameter, interpreted as a distance of a general solution from a Warnsdorff solution, we conjecture that $\G=1.22\times 10^{15}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
