Limited discrepancy search

Many problems of practical interest can be solved using tree search methods because carefully tuned successor ordering heuristics guide the search toward regions of the space that are likely to contain solutions. For some problems, the heuristics often lead directly to a solution— but not always. Limited discrepancy search addresses the problem of what to do when the heuristics fail. Our intuition is that a failing heuristic might well have succeeded if it were not for a small number of "wrong turns " along the way. For a binary tree of height d, there are only d ways the heuristic could make a single wrong turn, and only d(d-i)/2 ways it could make two. A small number of wrong turns can be overcome by systematically searching all paths that differ from the heuristic path in at most a small number of decision points, or "discrepancies." Limited discrepancy search is a backtracking algorithm that searches the nodes of the tree in increasing order of such discrepancies. We show formally and experimentally that limited discrepancy search can be expected to outperform existing approaches. 1