Encyclopedia of Optimization

2009 Edition
| Editors: Christodoulos A. Floudas, Panos M. Pardalos

Minimax Game Tree Searching

  • Claude G. Diderich
  • Marc Gengler
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-74759-0_370

Article Outline

Keywords

Minimax Trees

Sequential Minimax Game Tree Algorithms

  Minimax Algorithm

  Alpha-Beta Algorithm

  SSS∗

  SCOUT: Minimax Algorithm of Theoretical Interest

  Generalized Game Tree Search Algorithm

  Recursive State Space Search Algorithm

  Some Variations On The Subject

Parallel Minimax Tree Algorithms

  A Simple Way to Parallelize the Exploration of Minimax Trees

  A Mandatory Work First Algorithm

  Aspiration Search

  Tree-Splitting Algorithm

  Principal Variation Splitting Algorithm

  Distributed State Space Search

  Distributed Game Tree Search Algorithm

  Parallel Minimax Algorithm with Linear Speedup

See also

References

Keywords

Algorithms Games Minimax Searching 
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References

  1. 1.
    Akl SG, Barnard DT, Doran RJ (1979) Searching game trees in parallel. In: Proc. 3rd Biennial Conf. Canad. Soc. Computation Studies of Intelligence, pp 224–231Google Scholar
  2. 2.
    Akl SG, Barnard DT, Doran RJ (1982) Design, analysis, and implementation of a parallel tree search algorithm. IEEE Trans Pattern Anal Machine Intell PAMI-4(2):192–203CrossRefGoogle Scholar
  3. 3.
    Almquist K, McKenzie N, Sloan K (1988) An inquiry into parallel algorithms for searching game trees. Techn. Report Univ. Washington, Seattle, WA 12(3)Google Scholar
  4. 4.
    Althöfer I (1988) On the complexity of searching game trees and other recursion trees. J Algorithms 9:538–567MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Althöfer I (1990) An incremental negamax algorithm. Artif Intell 43:57–65CrossRefMATHGoogle Scholar
  6. 6.
    Ballard BW (1983) The ∗ -minimax search procedure for trees containing chance nodes. Artif Intell 21:327–350CrossRefMATHGoogle Scholar
  7. 7.
    Baudet GM (1978) The design and analysis of algorithms for asynchronous multiprocessors. PhD Thesis Carnegie-Mellon Univ. Pittsburgh, PA, CMU-CS-78-116Google Scholar
  8. 8.
    Böhm M, Speckenmeyer E (1989) A dynamic processor tree for solving game trees in parallel. Proc. SOR'89Google Scholar
  9. 9.
    Cung V-D, Roucairol C (1991) Parallel minimax tree searching. Res Report INRIA, vol 1549Google Scholar
  10. 10.
    Diderich CG (1992) Evaluation des performances de l'algorithme SSS∗ avec phases de synchronisation sur une machine parallèle à mémoires distribuées. Techn. Report Computer Sci. Dept. Swiss Federal Inst. Techn. Lausanne, Switzerland, LiTH-99 (In French.)Google Scholar
  11. 11.
    Feigenbaum EA, Feldman J (1963) Computers and thought. McGraw-Hill, New YorkMATHGoogle Scholar
  12. 12.
    Feldmann R, Monien B, Mysliwietz P, Vornberger O (1989) Distributed game tree search. ICCA J 12(2):65–73Google Scholar
  13. 13.
    Feldmann R, Mysliwietz P, Monien B (1994) Game tree search on a massively parallel system. In: van den Herik HJ, Herschberg IS, Uiterwijk JWHM (eds) Advances in Computer Chess, vol 7. Univ. Limburg, Maastricht, pp 203–218Google Scholar
  14. 14.
    Finkel RA, Fishburn JP (1982) Parallelism in alpha-beta search. Artif Intell 19:89–106MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Hewett R, Krishnamurthy G (1992) Consistent linear speedup in parallel alpha-beta search. Proc. ICCI'92, Computing and Information. IEEE Computer Soc Press, New York, pp 237–240Google Scholar
  16. 16.
    Ibaraki T (1986) Generalization of alpha-beta and {SSS*} search procedures. Artif Intell 29:73–117MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Karp RM, Zhang Y (1989) On parallel evaluation of game trees. In: ACM Annual Symp. Parallel Algorithms and Architectures (SPAA'89). ACM, New York, pp 409–420CrossRefGoogle Scholar
  18. 18.
    Knuth DE, Moore RW (1975) An analysis of alpha-beta pruning. Artif Intell, 6(4):293–326MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Marsland TA, Campbell MS (1982) Parallel search of strongly ordered game trees. ACM Computing Surveys 14(4):533–551CrossRefGoogle Scholar
  20. 20.
    Marsland TA, Popowich F (1985) Parallel game-tree search. IEEE Trans Pattern Anal Machine Intell PAMI-7(4):442–452CrossRefGoogle Scholar
  21. 21.
    Marsland TA, Reinefeld A, Schaeffer J (1987) Low overhead alternatives to SSS. Artif Intell 31:185–199CrossRefGoogle Scholar
  22. 22.
    McAllester DA (1988) Conspiracy numbers for min-max searching. Artif Intell 35:287–310MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Pearl J (1980) Asymptotical properties of minimax trees and game searching procedures. Artif Intell 14(2):113–138MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Pijls W, de Bruin A (Aug. 1990) Another view of the SSS∗ algorithm. In: Proc. Internat. Symp. (SIGAL'90)Google Scholar
  25. 25.
    Rivest RL (1987) Game tree searching by min/max approximation. Artif Intell 34(1):77–96MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Roizen I, Pearl J (1983) A minimax algorithm better than alpha-beta? Yes and no. Artif Intell 21:199–230MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Slagle JH, Dixon JK (Apr. 1969) Experiments with some programs that search game trees. J ACM 16(2):189–207CrossRefMATHGoogle Scholar
  28. 28.
    Steinberg IR, Solomon M (1990) Searching game trees in parallel. Proc. IEEE Internat. Conf. Parallel Processing, III, III–9–III–17Google Scholar
  29. 29.
    Stockman GC (1979) A minimax algorithm better than alpha-beta? Artif Intell 12(2):179–196MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Claude G. Diderich
    • 1
  • Marc Gengler
    • 2
  1. 1.Computer Sci. DepartmentSwiss Federal Institute Technology-LausanneLausanneSwitzerland
  2. 2.Ecole Sup. d'Ingénieurs de LuminyUniversité MéditerrannéeMarseilleFrance