Advertisement

A Solution to the GHI Problem for Best-First Search

  • Dennis M. Breuker
  • H. Jaap van den Herik
  • Jos W. H. M. Uiterwijk
  • L. Victor Allis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1558)

Abstract

In a search graph a node’s value may be dependent on the path leading to it. Different paths may lead to different values. Hence, it is difficult to determine the value of any node unambiguously. The problem is known as the graph-history-interaction (GHI) problem. This paper provides a solution for best-first search. First, we give a precise formulation of the problem. Then, for best-first search and for other searches, we review earlier proposals to overcome the problem. Next, our solution is given in detail. Here we introduce the notion of twin nodes, enabling a distinction of nodes according to their history. The implementation, called BTA (Base-Twin Algorithm), is performed for pn search, a best-first search algorithm. It is generally applicable to other best-first search algorithms. Experimental results in the field of computer chess confirm the claim that the GHI problem has been solved for best-first search.

Keywords

graph-history interaction (GHI) problem best-first search base-twin algorithm (BTA) 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L.V. Allis, M. van der Meulen, and H.J. van den Herik. Proof-Number Search. Artificial Intelligence, 66(1):91–124, 1994.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    L.V. Allis. Searching for Solutions in Games and Artificial Intelligence. Ph.D. thesis, University of Limburg, Maastricht, The Netherlands, 1994.Google Scholar
  3. 3.
    E.B. Baum and W.D. Smith. Best Play for Imperfect Players and Game Tree Search. Submitted to Artificial Intelligence.Google Scholar
  4. 4.
    H.J. Berliner and C. McConnell. B* Probability Based Search. Artificial Intelligence, 86(1):97–156, 1996.CrossRefGoogle Scholar
  5. 5.
    D.M. Breuker, L.V. Allis, and H.J. van den Herik. How to Mate: Applying Proof-Number Search. In H.J. van den Herik, I.S. Herschberg, and J.W.H.M. Uiterwijk, editors, Advances in Computer Chess 7, pages 251–272, Maastricht, The Netherlands, 1994. University of Limburg.Google Scholar
  6. 6.
    D.M. Breuker, H.J. van den Herik, L.V. Allis, and J.W.H.M. Uiterwijk. A Solution to the GHI Problem for Best-First Search. Technical Report #CS 97-02, Computer Science Department, Universiteit Maastricht, Maastricht, The Netherlands, 1997.Google Scholar
  7. 7.
    D.M. Breuker. Memory versus Search in Games. Ph.D. thesis, Universiteit Maastricht, The Netherlands, 1998.Google Scholar
  8. 8.
    M. Campbell. The Graph-History Interaction: On Ignoring Position History. In 1985 Association for Computing Machinery Annual Conference, pages 278–280, 1985.Google Scholar
  9. 9.
    R.M. Hyatt, A.E. Gower, and H.L. Nelson. Cray Blitz. In D.F. Beal, editor, Advances in Computer Chess 4, pages 8–18, Oxford, United Kingdom, 1984. Pergamon Press.Google Scholar
  10. 10.
    B. Kaйzić, R. Keene, and K.A. Lim. The Official Laws of Chess and Other FIDE Regulations. B.T. Batsford Ltd., London, United Kingdom, 1985.Google Scholar
  11. 11.
    T. Krabbé. Chess Curiosities. George Allen and Unwin Ltd., London, United Kingdom, 1985.Google Scholar
  12. 12.
    T.A. Marsland. A Review of Game-Tree Pruning. ICCA Journal, 9(1):3–19, 1986.Google Scholar
  13. 13.
    A.J. Palay. Searching with Probabilities. Ph.D. thesis, Boston University, Boston MA, USA, 1985.MATHGoogle Scholar
  14. 14.
    A. Plaat, J. Schaeffer, W. Pijls, and A. de Bruin. Best-First Fixed-Depth Minimax Algorithms. Artificial Intelligence, 87(2):255–293, 1996.CrossRefMathSciNetGoogle Scholar
  15. 15.
    F. Reinfeld. Win at Chess. Dover Publications Inc., New York NY, USA, 1958. Originally published (1945) as Chess Quiz by David McKay Company, New York NY, USA.Google Scholar
  16. 16.
    M. Schijf. Proof-Number Search and Transpositions. M.Sc. thesis, University of Leiden, Leiden, The Netherlands, 1993.Google Scholar
  17. 17.
    M. Schijf, L.V. Allis, and J.W.H.M. Uiterwijk. Proof-Number Search and Transpositions. ICCA Journal, 17(2):63–74, 1994.Google Scholar
  18. 18.
    G. Stockman. A Minimax Algorithm Better than Alpha-beta? Artificial Intelligence, 12:179–196, 1979.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    K. Thompson. Personal communication, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Dennis M. Breuker
    • 1
  • H. Jaap van den Herik
    • 1
  • Jos W. H. M. Uiterwijk
    • 1
  • L. Victor Allis
    • 2
  1. 1.Department of Computer ScienceUniversiteit MaastrichtMD MaastrichtThe Netherlands
  2. 2.Quintiq B.V.AV’ s HertogenboschThe Netherlands

Personalised recommendations