Warnsdorff的骑士之旅启发式有多好？
How good is the Warnsdorff's knight's tour heuristic?
摘要：
Warnsdorff规则对于骑士之旅是一种启发式的，即，这是一条并不总是产生预期结果的规则。这是一个经典的例子，贪婪的方法，因为它是基于一系列的局部最优选择。本文描述了一个分析，确定如何好的启发式是在一个8 × 8的棋盘。骑士可以进行的八种可能移动的排列中出现的顺序决定了骑士采取的路径。计算机分析的8！排列顺序的一个骑士行动在Warnsdorff规则上的8 × 8棋盘上的旅游开始的每一个64个广场。每当移动到具有最低度数的顶点时出现平局时，选择编程循环中遇到的这些顶点中的第一个。8的排列数！计算产生非哈密顿路径的总和。如果我们始终选择遇到的最后一个顶点，这将是相同的值。
英文摘要：
Warnsdorffs rule for a knights tour is a heuristic, i.e., it is a rule that does not produce the desired result all the time. It is a classic example of a greedy method in that it is based on a series of locally optimal choices. This note describes an analysis that determines how good the heuristic is on an 8 X 8 chessboard. The order of appearance in a permutation of the eight possible moves a knight can make determines the path the knight takes. A computer analysis is done of the 8! permutations of the order of a knights moves in Warnsdorffs rule on an 8 X 8 chessboard for tours starting on each of the 64 squares. Whenever a tie occurs for moves to vertices that have the lowest degree, the first of these vertices encountered in the programming loop is chosen. The number of permutations of the 8! total that yield non-Hamiltonian paths is tallied. This will be the same value if we consistently choose the last of these vertices encountered.
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。
