An Algorithm for Colouring Additive Puzzles

Abstract

Additive puzzles form a large and important class of problems in Artificial Intelligence, since many other problems may be shown to be homomorphic to them, and many techniques for solving them are easily transferable to certain classes of problems. For many additive puzzles, a homomorphic puzzle can be sometimes obtained which is much simpler than the initial one. If the simple puzzle cannot be solved from the image of a state in the first puzzle, then the first puzzle cannot be solved from that state. A method to obtain a simple homomorphic puzzle is by colouring its board. This paper presents an algorithm for colouring the boards of additive puzzles. Three heuristic backtracking decisions are discussed and their experimental performances are compared.