Skip to main content

Feature Strength and Parallelization of Sibling Conspiracy Number Search

  • Conference paper
  • First Online:
  • 630 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9525))

Abstract

Recently we introduced Sibling Conspiracy Number Search — an algorithm based not on evaluation of leaf states of the search tree but, for each node, on relative evaluation scores of all children of that node — and implemented an SCNS Hex bot. Here we show the strength of SCNS features: most critical is to initialize leaves via a multi-step process. Also, we show a simple parallel version of SCNS: it scales well for 2 threads but less efficiently for 4 or 8 threads.

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

Buying options

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 EPUB and 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

Learn about institutional subscriptions

Notes

  1. 1.

    Hex has a good local heuristic. Shannon built an analogue circuit to play the connection game Bridg-it, with moves scored by voltage drop [7]. Adding links between virtual connected cells [2] improves the heuristic, which is reliable among siblings [9].

  2. 2.

    This is the current likely range of the final root minimax value. It is analogous to the aspiration window of \(\alpha \beta \) search.

  3. 3.

    Another approach is to dynamically partition the CNS tree and evaluate subproblems in parallel. Lorenz achieved this for the restriction of CNS to 2 conpirators, i.e., effectively bounding proof function numbers at 2 [14].

References

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

    Google Scholar 

  2. Anshelevich, V.V.: A hierarchical approach to computer Hex. Artif. Intell. 134(1–2), 101–120 (2002)

    Article  MATH  Google Scholar 

  3. Arneson, B., Henderson, P., Hayward, R.B.: Benzene (2009). http://benzene.sourceforge.net/

  4. Breuker, D.M.: Memory versus Search in Games. PhD thesis, Maastricht University, Maastricht, The Netherlands (1998)

    Google Scholar 

  5. Coulom, R.: Bayesian elo rating (2010). http://remi.coulom.free.fr/Bayesian-Elo

  6. Coulom, R.: CLOP: confident local optimization for noisy black-box parameter tuning. In: van den Herik, H.J., Plaat, A. (eds.) ACG 2011. LNCS, vol. 7168, pp. 146–157. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  7. Gardner, M.: The 2nd scientific american book of mathematical puzzles and diversions, Chap. 7, pp. 78–88. Simon and Schuster, New York (1961)

    Google Scholar 

  8. Gelly, S., Silver, D.: Combining online and offline knowledge in UCT. In: 24th ACM ICML, pp. 273–280 (2007)

    Google Scholar 

  9. Henderson, P.: Playing and solving Hex. PhD thesis, UAlberta (2010). http://webdocs.cs.ualberta.ca/~hayward/theses/ph.pdf

  10. Huang, S.-C., Arneson, B., Hayward, R.B., Müller, M., Pawlewicz, J.: MoHex 2.0: a pattern-based MCTS Hex player. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) CG 2013. LNCS, vol. 8427, pp. 60–71. Springer, Heidelberg (2014)

    Google Scholar 

  11. Iida, H., Sakuta, M., Rollason, J.: Computer shogi. Artif. Intell. 134(1–2), 121–144 (2002)

    Article  MATH  Google Scholar 

  12. Kishimoto, A., Winands, M., Müller, M., Saito, J.-T.: Game-tree searching with proof numbers: the first twenty years. ICGA J. 35(3), 131–156 (2012)

    Article  Google Scholar 

  13. Klingbeil, N., Schaeffer, J.: Empirical results with conspiracy numbers. Comput. Intell. 6, 1–11 (1990)

    Article  Google Scholar 

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

    Chapter  Google Scholar 

  15. Lorenz, U., Rottmann, V., Feldman, R., Mysliwietz, P.: Controlled conspiracy number search. ICCA J. 18(3), 135–147 (1995)

    Google Scholar 

  16. McAllester, D.: Conspiracy numbers for min-max search. Artif. Intell. 35(3), 287–310 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  17. McAllester, D., Yuret, D.: Alpha-beta conspiracy search. ICGA 25(1), 16–35 (2002)

    Google Scholar 

  18. Nagai, A.: Df-pn Algorithm for Searching AND/OR Trees and Its Applications. Ph.d. thesis, Department of Information Science, University Tokyo, Tokyo, Japan (2002)

    Google Scholar 

  19. Pawlewicz, J., Hayward, R.: Sibling conspiracy number search. manuscript (2015)

    Google Scholar 

  20. Pawlewicz, J., Hayward, R.B.: Scalable parallel DFPN search. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) CG 2013. LNCS, vol. 8427, pp. 138–150. Springer, Heidelberg (2014)

    Google Scholar 

  21. Pawlewicz, J., Lew, Ł.: Improving depth-first PN-search: 1 + \(\epsilon \) trick. In: van den Herik, H.J., Ciancarini, P., Donkers, H.H.L.M.J. (eds.) CG 2006. LNCS, vol. 4630, pp. 160–171. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  22. Saito, J.-T., Chaslot, G.M.J.-B., Uiterwijk, J.W.H.M., van den Herik, H.J.: Monte-Carlo proof-number search for computer Go. In: van den Herik, H.J., Ciancarini, P., Donkers, H.H.L.M.J. (eds.) CG 2006. LNCS, vol. 4630, pp. 50–61. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  23. Schaeffer, J.: Conspiracy numbers. Artif. Intell. 43(1), 67–84 (1990)

    Article  MathSciNet  Google Scholar 

  24. van der Meulen, M.: Parallel conspiracy-number search. Master’s thesis, Vrije Universiteit Amsterdam, The Netherlands (1988)

    Google Scholar 

  25. Winands, M.: Informed Search in Complex Games. PhD thesis, Universiteit Maastricht, Maastricht, The Netherlands (2004)

    Google Scholar 

  26. Winands, M.H.M., Schadd, M.P.D.: Evaluation-function based proof-number search. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) CG 2010. LNCS, vol. 6515, pp. 23–35. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ryan B. Hayward .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Pawlewicz, J., Hayward, R.B. (2015). Feature Strength and Parallelization of Sibling Conspiracy Number Search. In: Plaat, A., van den Herik, J., Kosters, W. (eds) Advances in Computer Games. ACG 2015. Lecture Notes in Computer Science(), vol 9525. Springer, Cham. https://doi.org/10.1007/978-3-319-27992-3_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27992-3_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27991-6

  • Online ISBN: 978-3-319-27992-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics