Skip to main content

Randomized Parallel Proof-Number Search

  • Conference paper
Advances in Computer Games (ACG 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6048))

Included in the following conference series:

Abstract

Proof-Number Search (PNS) is a powerful method for solving games and game positions. Over the years, the research on PNS has steadily produced new insights and techniques. With multi-core processors becoming established in the recent past, the question of parallelizing PNS has gained new urgency. This article presents a new technique called Randomized Parallel Proof-Number Search (RPPNS) for parallelizing PNS on multi-core systems with shared memory. The parallelization is based on randomizing the move selection of multiple threads, which operate on the same search tree. RPPNS is tested on a set of complex Lines-of-Action endgame positions. Experiments show that RPPNS scales well. Four directions for future research are given.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Allis, L.V., van der Meulen, M., van den Herik, H.J.: Proof-Number Search. Artificial Intelligence 66(1), 91–124 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. Allis, L.V.: Searching for Solutions in Games and Artificial Intelligence. PhD thesis, Rijksuniversiteit Limburg, Maastricht, The Netherlands (1994)

    Google Scholar 

  3. Nagai, A.: A new depth-first search algorithm for AND/OR trees. In: Matsubara, H., Kotani, Y., Takizawa, T., Yoshikawa, A. (eds.) Proceedings of the Complex Games Lab Workhshop, ETL, Tsuruoka, Japan, pp. 40–45 (1998)

    Google Scholar 

  4. Nagai, A.: Df-pn algorithm for searching AND/OR trees and its applications. PhD thesis, University of Tokyo, Japan (2002)

    Google Scholar 

  5. Seo, M., Iida, H., Uiterwijk, J.W.H.M.: The \(\mbox{PN}^{\ast}\)-Search algorithm: application to tsume shogi. Artificial Intelligence 129(1-2), 253–277 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kishimoto, A., Müller, M.: DF-PN in Go: Application to the one-eye problem. In: van den Herik, H.J., Iida, H., Heinz, E. (eds.) Proceedings of the 10th Advances in Computer Games Conference (ACG 2003), Norwell, MA, USA, vol. 10, pp. 125–141. Kluwer Academic, Dordrecht (2003)

    Google Scholar 

  7. Schaeffer, J., Burch, N., Björnsson, Y., Kishimoto, A., Müller, M., Lake, R., Lu, P., Sutphen, S.: Checkers is solved. Science 317(5844), 1518–1522 (2007)

    Article  MathSciNet  Google Scholar 

  8. Winands, M.H.M., Uiterwijk, J.W.H.M., van den Herik, H.J.: PDS-PN: A new proof-number search algorithm: application to Lines of Action. In: Schaeffer, J., Müller, M., Björnsson, Y. (eds.) CG 2002. LNCS, vol. 2883, pp. 170–185. Springer, Heidelberg (2003)

    Google Scholar 

  9. Brockington, M.: A taxonomy of parallel game-tree search algorithms. ICCA Journal 19(3), 162–174 (1996)

    Google Scholar 

  10. Kishimoto, A., Kotani, Y.: Parallel AND/OR tree search based on proof and disproof numbers. In: Proceedings of the 5th Game Programming Workshop, Hakone, Japan. IPSJ Symposium Series, vol. 99(14), pp. 24–30 (1999)

    Google Scholar 

  11. Breuker, D.: Memory versus search. PhD thesis, Maastricht University, The Netherlands (1998)

    Google Scholar 

  12. Brockington, M., Schaeffer, J.: APHID Game-Tree Search. In: van den Herik, H., Uiterwijk, J. (eds.) Advances in Computer Chess, Univeriseit Maastricht, vol. 8, pp. 69–92 (1997)

    Google Scholar 

  13. McAllester, D.: Conspiracy numbers for min-max search. Artificial Intelligence 35(3), 287–310 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lorenz, U.: Parallel controlled conspiracy number search. In: Monien, M., Feldmann, R. (eds.) Euro-Par 2002. LNCS, vol. 2400, pp. 420–430. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  15. Shoham, Y., Toledo, S.: Parallel randomized best-first minimax search. Artificial Intelligence 137(1-2), 165–196 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  16. Buro, M.: Toward opening book learning. ICCA Journal 22, 98–102 (1999)

    Google Scholar 

  17. Chaslot, G., Winands, M.H.M., van den Herik, H.J.: Parallel Monte-Carlo Tree Search. In: van den Herik, H.J., Xu, X., Ma, Z., Winands, M.H.M. (eds.) CG 2008. LNCS, vol. 5131, pp. 60–71. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  18. Cazenave, T., Jouandeau, N.: On the Parallelization of UCT. In: van den Herik, H.J., Uiterwijk, J.W.H.M., Winands, M.H.M., Schadd, M. (eds.) Computer Games Workshop (CGW 2007). MICC Technical Report Series, vol. 07-06, pp. 93–101. Maastricht University, Maastricht (2007)

    Google Scholar 

  19. Pawlewicz, J., Lew, L.: Improving depth-first pn-search: 1+ε trick. In: van den Herik, H.J., Ciancarini, P., Donkers, H.H.L.M(J.) (eds.) CG 2006. LNCS, vol. 4630, pp. 160–170. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  20. van den Herik, H.J., Winands, M.H.M.: Proof-Number search and its variants. In: Tizhoosh, H., Ventresca, M. (eds.) Oppositional Concepts in Computational Intelligence. Studies in Computational Intelligence, vol. 155, pp. 91–118. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Saito, JT., Winands, M.H.M., van den Herik, H.J. (2010). Randomized Parallel Proof-Number Search. In: van den Herik, H.J., Spronck, P. (eds) Advances in Computer Games. ACG 2009. Lecture Notes in Computer Science, vol 6048. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12993-3_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12993-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12992-6

  • Online ISBN: 978-3-642-12993-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics