Generating Hamiltonian circuits without backtracking from errors

Abstract

We describe research on the problem of generating multiple closed tours of an m × n chessboard by a knight, subject to the constraint that the search scheme used to solve the problem is nonbacktracking; i.e. that the search engine never visits a node in the search tree that will ultimately lead to a dead end. We describe our experiences and results in the context ofKTC (Knight's Tour, Chess), a search program developed to undertake this task. We describe the implementation ofktc and the search constraints we discovered, which apply to all Hamiltonian circuit graph search problems. We discussKTC's performance to date, illustrating that a limited amount of domain knowledge can lead to near-perfect search on this class of Hamiltonian circuit construction problems. We close by suggesting promising directions for achieving a perfect search on this problem and the implications of such an achievement.