Skip to main content
SpringerLink
Log in

An upper bound on the time complexity of iterative-deepening-A*

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

This paper establishes an upper bound on the time complexity of iterative-deepening-A* (IDA*) in terms of the number of states that are surely-expanded by A* during a state space tree search. It is shown that given an admissible evaluation function, IDA* surely-expands in the worst caseN(N+1)/2 states, whereN is the number of states that are surely-expanded by A*. The conditions that give rise to the worst case performance of IDA* on any state space tree are described. Worst case examples are also given for uniform and non-uniform state space trees.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Google Scholar 

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

    Google Scholar 

  3. A. Bagchi and A.K. Sen, Average-case analysis of heuristic search in tree-like networks, in:Search in Artificial Intelligence, eds. L. Kanal and V. Kumar (Springer, New York, 1988) pp. 131–165.

    Google Scholar 

  4. R. Dechter and J. Pearl, The optimality of A* revisited,Proc. 3rd AAAI Conf., Washington, DC (1983) pp. 95–99.

  5. R. Dechter and J. Pearl, Generalized best-first search strategies and the optimality of A*, J. ACM 32 (1989) 505–536.

    Google Scholar 

  6. R. Dechter and J. Pearl, The optimality of A*, in:Search in Artificial Intelligence, eds. L. Kanal and V. Kumar (Springer, New York, 1988) pp. 166–199.

    Google Scholar 

  7. J. Gaschnig, Performance measurement and analysis of certain search algorithms, Ph.D. dissertation, Technical Report CMU-CS-79-124, Computer Science Department, Carnegie Mellon University, Pittsburgh, PA (1979).

    Google Scholar 

  8. D. Gelperin, On the optimality of A*, Art. Int. 8 (1977) 69–76.

    Google Scholar 

  9. P.E. Hart, N.J. Nilsson and B. Raphael, A formal basis for the heuristic determination of minimum cost paths, IEEE Trans. Systems Sci. Cyber. SSC-4 (1968) 100–107.

    Google Scholar 

  10. P.E. Hart, N.J. Nilsson and B. Raphael, Correction to “A formal basis for the heuristic determination of minimum cost paths”, SIGART Newsletter 37 (1972) 28–29.

    Google Scholar 

  11. N. Huyn, R. Dechter and J. Pearl, Probabilistic analysis of the complexity of A*, Art. Int. 15 (1980) 241–254.

    Google Scholar 

  12. R.E. Korf, Depth-first iterative-deepening: An optimal admissible tree search, Art. Int. 27 (1985) 97–109.

    Google Scholar 

  13. R.E. Korf, Optimal path-finding algorithms, in:Search in Artificial Intelligence, eds. L. Kanal and V. Kumar (Springer, New York, 1988) pp. 223–267.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  16. L. Mérõ, A heuristic search algorithm with modifiable estimate, Art. Int. 23 (1984) 13–27.

    Google Scholar 

  17. N.J. Nilsson,Problem Solving Methods in Artificial Intelligence (McGraw-Hill, New York, 1971).

    Google Scholar 

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

  19. B.G. Patrick, An analysis of iterative-deepening-A*, Ph.D. dissertation, School of Computer Science, McGill University, Montréal, Québec, Canada (1991).

    Google Scholar 

  20. J. Pearl, Knowledge versus search: A quantitative analysis using A*, Art. Int. 20 (1983) 1–13.

    Google Scholar 

  21. J. Pearl,Intelligent Search Strategies for Computer Problem Solving (Addison-Wesley, Menlo Park, CA, 1984).

    Google Scholar 

  22. I. Pohl, First results on the effect of error in heuristic search, in:Machine Intelligence 5, eds. B. Meltzer and D. Michie (American Elsevier, New York, 1970) pp. 219–236.

    Google Scholar 

  23. I. Pohl, Heuristic search viewed as path finding in a graph, Art. Int. 1 (1970) 193–204.

    Google Scholar 

  24. I. Pohl, The avoidance of (relative) catastrophe, heuristic competence, genuine dynamic weighting and computational issues in heuristic problem solving,Proc. IJCAI 3, Stanford, CA (1973) pp. 20–23.

  25. I. Pohl, Practical and theoretical considerations in heuristic search algorithms, in:Machine Intelligence 8, eds. E.W. Elcock and D. Michie (Wiley, New York, 1977) pp. 55–72.

    Google Scholar 

Download references

Author information

Author notes

  1. Brian G. Patrick

    Present address: Department of Computer Science and Engineering, Collège Militaire Royal, JOJ 1R0, Richelain, Quebec, Canada

Authors and Affiliations

  1. School of Computer Science, McGill University, Montréal, Québec, Canada

    Brian G. Patrick, Mohammed Almulla & Monroe M. Newborn

Authors
  1. Brian G. Patrick
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammed Almulla
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Monroe M. Newborn
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported in part by the Canadian Natural Sciences and Engineering Research Council Grant NSERC3599.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Patrick, B.G., Almulla, M. & Newborn, M.M. An upper bound on the time complexity of iterative-deepening-A* . Ann Math Artif Intell 5, 265–277 (1992). https://doi.org/10.1007/BF01543478

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01543478

Keywords

Search

Navigation