Recent Progress in the Design and Analysis of Admissible Heuristic Functions

  • Richard E. Korf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1864)


In the past several years, significant progress has been made in finding optimal solutions to combinatorial problems. In particular, random instances of both Rubik’s Cube, with over 1019 states, and the 5×5 sliding-tile puzzle, with almost 1025 states, have been solved optimally. This progress is not the result of better search algorithms, but more effective heuristic evaluation functions. In addition, we have learned how to accurately predict the running time of admissible heuristic search algorithms, as a function of the solution depth and the heuristic evaluation function. One corollary of this analysis is that an admissible heuristic function reduces the effective depth of search, rather than the effective branching factor.


Problem Instance Pairwise Distance Heuristic Function Manhattan Distance Random Instance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Culberson, J., and J. Schaeffer. Pattern Databases, Computational Intelligence, Vol. 14, No. 3, 1998, pp. 318–334.CrossRefMathSciNetGoogle Scholar
  2. 2.
    Edelkamp, S. and R.E. Korf, The branching factor of regular search spaces, Proceedings of the National Conference on Artificial Intelligence (AAAI-98), Madison, WI, July, 1998, pp. 299–304.Google Scholar
  3. 3.
    Hansson, O., A. Mayer, and M. Yung, Criticizing solutions to relaxed models yields powerful admissible heuristics, Information Sciences, Vol. 63, No. 3, 1992, pp. 207–227.CrossRefGoogle Scholar
  4. 4.
    Hart, P.E., N.J. Nilsson, and B. Raphael, A formal basis for the heuristic determination of minimum cost paths, IEEE Transactions on Systems Science and Cybernetics, Vol. SSC-4, No. 2, July 1968, pp. 100–107.CrossRefGoogle Scholar
  5. 5.
    Johnson, W.W. and W.E. Storey, Notes on the 15 puzzle, American Journal of Mathematics, Vol. 2, 1879, pp. 397–404.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Korf, R.E., Depth-first iterative-deepening: An optimal admissible tree search, Artificial Intelligence, Vol. 27, No. 1, 1985, pp. 97–109.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Korf, R.E., and L.A. Taylor, Finding optimal solutions to the twenty-four puzzle, Proceedings of the National Conference on Artificial Intelligence (AAAI-96), Portland, OR, Aug. 1996, pp. 1202–1207.Google Scholar
  8. 8.
    Korf, R.E., Finding optimal solutions to Rubik’s Cube using pattern databases, Proceedings of the National Conference on Artificial Intelligence (AAAI-97), Providence, RI, July, 1997, pp. 700–705.Google Scholar
  9. 9.
    Korf, R.E., and M. Reid, Complexity analysis of admissible heuristic search, Proceedings of the National Conference on Artificial Intelligence (AAAI-98), Madison, WI, July, 1998, pp. 305–310.Google Scholar
  10. 10.
    Loyd, S., Mathematical Puzzles of Sam Loyd, selected and edited by Martin Gardner, Dover, New York, 1959.Google Scholar
  11. 11.
    Pearl, J. Heuristics, Addison-Wesley, Reading, MA, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Richard E. Korf
    • 1
  1. 1.Computer Science DepartmentUniversity of California, Los AngelesLos Angeles

Personalised recommendations