Heuristics for the Sudoku Distances Problem

Science Center, Bent Corridor

The Sudoku Distances Problem (or SDP) is a graph theoretic problem which asks for the minimum-weight Hamiltonian path through a complete weighted graph, from a specified start vertex. Edges in SDP instances are weighted according to the "Manhattan distance" between their endpoints. The SDP is a variation of the Traveling Salesman Problem, which holds importance in complexity theory and the whole of computer science. We use graph theoretic methods to analyze general instances of the SDP and their solutions. We show that a solution to an arbitrary instance of the SDP (i.e. a minimum-weight path) never needs to cross itself in its geometric representation, and present a heuristic for the SDP which utilizes that result by avoiding paths which cross themselves. We present another heuristic which takes advantage of the properties of spaces which use "Manhattan distance" as a]their distance metric.