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On the asymptotic performance of IDA*

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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 Ω(22N) node expansions where N is the number of nodes expanded by A*.

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References

  1. A. Bagchi and A. Mahanti, Search algorithms under different kinds of heuristics — a comparative study, JACM 30(1) (1983) 1–21.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Bagchi and A. Mahanti, Three approaches to heuristic search in networks, JACM 32(1) (1985) 1–27.

    Article  MATH  MathSciNet  Google Scholar 

  3. P.P. Chakrabarti, S. Ghosh, A. Acharya and S.C. De Sarkar, Heuristic search in restricted memory, Artificial Intelligence 47 (1989) 197–221.

    Article  Google Scholar 

  4. R. Dechter and J. Pearl, Generalized best-first search strategies and the optimality of A*, JACM 32(3) (1985) 505–536.

    Article  MATH  MathSciNet  Google Scholar 

  5. M. Evett, J. Hendler, A. Mahanti and D. Nau, PRA*: A memory-limited heuristic search procedure for the connection machine, in: Frontiers '90: Frontiers of Massively Parallel Computation (1990).

  6. S. Ghosh, A. Mahanti and D.S. Nau, ITS: An efficient limited-memory heuristic tree search algorithm, in: AAAI 1994 (1994) pp. 1353–1358.

  7. P.E. Hart, N.J. Nilsson and B. Raphael, A formal basis for the heuristic determination of minimum cost paths, IEEE Transactions on Systems Sciences and Cybernetics (1968) pp. 1556–1562.

  8. R. Korf, Linear-space best-first search, Artificial Intelligence 62 (1993) 41–78.

    Article  MATH  MathSciNet  Google Scholar 

  9. R.E. Korf, Depth first iterative deepening: An optimal admissible tree search, Artificial Intelligence 27 (1985) 97–109.

    Article  MATH  MathSciNet  Google Scholar 

  10. R.E. Korf, Optimal path finding algorithms, in: Search in Artificial Intelligence, eds. L. Kanal and V. Kumar (Springer-Verlag, 1988) pp. 200–222.

  11. J.D. Little, K.G. Murty, D.W. Sweeney and C. Karel, An algorithm for the traveling salesman problem, Operations Research 11 (1963) 972–989.

    Article  MATH  Google Scholar 

  12. A. Mahanti, S. Ghosh, D.S. Nau, A.K. Pal and L.N. Kanal, Performance of IDA* on trees and graphs, in: AAAI 1992 (1992) pp. 539–544.

  13. A. Mahanti and A.K. Pal, Worst-case time complexity of IDA*, in: Tenth International Conference in Computer Science (Santiago, Chile, July 1990).

  14. A. Mahanti and K. Ray, Network search algorithms with modifiable heuristics, in: Search in Artificial Intelligence, eds. L. Kanal and V. Kumar (Springer-Verlag, 1988) pp. 200–222.

  15. A. Martelli, On the complexity of admissible search algorithms, Artificial Intelligence 8 (1977) 1–13.

    Article  MATH  MathSciNet  Google Scholar 

  16. L. Mero, A heuristic search algorithm with modifiable estimate, Artificial Intelligence 23 (1984) 13–27.

    Article  MATH  MathSciNet  Google Scholar 

  17. N.J. Nilsson, Principles of Artificial Intelligence (Tioga, Palo Alto, 1980).

  18. B.G. Patrick, M. Almulla and M.M. Newborn, An upper bound on the complexity of iterative-deepening-A*, Annals of Mathematics and Artificial Intelligence 5 (1992) 265–278.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. Pearl, Heuristics (Addison-Wesley, Reading, MA, 1984).

    Google Scholar 

  20. S. Russell, Efficient memory-bounded search methods, in: ECAI-1992 (Vienna, Austria, 1992).

  21. A. Sen and A. Bagchi, Fast recursive formulations for best-first search that allow controlled use of memory, in: IJCAI-89 (1989) pp. 274–277.

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Authors and Affiliations

  1. IIM, Calcutta, Diamond Harbour Road, PO. Box No. 16757, Calcutta, 700 027, India

    A. Mahanti & A.K. Pal

  2. Hughes STX Corporation, 7701 Greenbelt Road, Suite 400, Greenbelt, MD, 20770, USA

    S. Ghosh

  3. Department of Computer Science, Institute for Systems Research, and Institute for Advanced Computer Studies, University of Maryland, College Park, MD, 20742, USA

    D.S. Nau

  4. Department of Computer Science, University of Maryland, College Park, MD, 20742, USA

    L.N. Kanal

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  1. A. Mahanti
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  2. S. Ghosh
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  3. D.S. Nau
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  4. A.K. Pal
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  5. L.N. Kanal
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Mahanti, A., Ghosh, S., Nau, D. et al. On the asymptotic performance of IDA*. Annals of Mathematics and Artificial Intelligence 20, 161–193 (1997). https://doi.org/10.1023/A:1018980327559

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