On the asymptotic performance of IDA*

  • Authors:

  • A. Mahanti;S. Ghosh;D. S. Nau;A. K. Pal;L. N. Kanal

  • Affiliations:

  • IIM, Calcutta, Diamond Harbour Road, PO. Box No. 16757, Calcutta 700 027, India;Hughes STX Corporation, 7701 Greenbelt Road, Suite 400, Greenbelt, MD 20770, USA E‐mail: subrata@cs.umd.edu;Department of Computer Science, Institute for Systems Research, and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, USA E‐mail: nau@cs. ...;IIM, Calcutta, Diamond Harbour Road, PO. Box No. 16757, Calcutta 700 027, India;Department of Computer Science, University of Maryland, College Park, MD 20742, USA E‐mail: kanal@cs.umd.edu

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 1997

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Abstract

Since best‐first 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 limited‐memory 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 [R.E. Korf, Optimal path finding algorithms, in: Search in Artificial Intelligence, eds. L. Kanal and V. Kumar (Springer‐Verlag, 1988) pp. 200–222] is incorrect. There are trees satisfying the asymptotic optimality conditions given in [R.E. Korf, Optimal path finding algorithms, in: Search in Artificial Intelligence, eds. L. Kanal and V. Kumar (Springer‐Verlag, 1988) pp. 200–222] 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 best‐first limited‐memory 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*.