On the asymptotic performance of IDA

Abstract

Since bestdfirst search algorithms such as A* require large amounts of memory, they sometimes cannot run to completion, even on problem instances of moderate size. This problem has led to the development of limiteddmemory search algorithms, of which the best known is IDA*. This paper presents the following results about IDA* and related algorithms: 1) The analysis of asymptotic optimality for IDA* in lR.E. Korf, Optimal path finding algorithms, in: Search in Artificial Intelligence, eds. L. Kanal and V. Kumar (SpringerdVerlag, 1988) pp. 200–222r is incorrect. There are trees satisfying the asymptotic optimality conditions given in lR.E. Korf, Optimal path finding algorithms, in: Search in Artificial Intelligence, eds. L. Kanal and V. Kumar (SpringerdVerlag, 1988) pp. 200–222r for which IDA* is not asymptotically optimal. 2) To correct the above problem, we state and prove necessary and sufficient conditions for asymptotic optimality of IDA* on trees. On trees not satisfying our conditions, we show that no bestdfirst limiteddmemory search algorithm can be asymptotically optimal. 3) On graphs, IDA* can perform quite poorly. In particular, there are graphs on which IDA* does \Omega(2^{2N}) node expansions where N is the number of nodes expanded by A*.