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Heuristic Strategies for the Knight Tour Problem

This paper presents three heuristic functions that aim to reduce the search cost for the knight tour problem. The first heuristic, h1a, is an interesting case of study that illustrates heuristic analysis, although it fails to obtain solutions. Heuristic h2 is an enhancement of the Warnsdorff method, discussed as heuristic h1b. All heuristics are used in conjunction with a greedy algorithm to decide which node to expand next on a best-first basis. Tests show that heuristics h1b and h2 narrow the search space considerably, in most cases to O(N) time when no backtracking occurs. However, the Warnsdorff method, h1b, fails on some boards, sharply declining as N grows larger. Heuristic h2 adds a new criterion to address this issue, being capable of finding complete tours on very large boards in O(N).