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Scalable Parallel DFPN Search

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Computers and Games (CG 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8427))

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Abstract

We present Scalable Parallel Depth-First Proof Number Search, a new shared-memory parallel version of depth-first proof number search. Based on the serial DFPN \(1+\varepsilon \) method of Pawlewicz and Lew, SPDFPN searches effectively even as the transposition table becomes almost full, and so can solve large problems. To assign jobs to threads, SPDFPN uses proof and disproof numbers and two parameters. SPDFPN uses no domain-specific knowledge or heuristics, so it can be used in any domain. Our experiments show that SPDFPN scales well and performs well on hard problems.

We tested SPDFPN on problems from the game of Hex. On a 24-core machine and a 4.2-hour single-thread task, parallel efficiency ranges from 0.8 on 4 threads to 0.74 on 16 threads. SPDFPN solved all previously intractable 9 \(\times \) 9 Hex opening moves; the hardest opening took 111 days. Also, in 63 days, it solved one 10 \(\times \) 10 Hex opening move. This is the first time a computer or human has solved a 10 \(\times \) 10 Hex opening move.

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Notes

  1. 1.

    Do not confuse Kaneko’s augmented proof/disproof values with our definition of virtual pn.

  2. 2.

    Private communication with Broderick Arneson.

  3. 3.

    As usual when measuring a ratio (here, speedup), we use geometric mean for averaging.

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Acknowledgements

We thank Broderick Arneson, Yngvi Björnsson, Phil Henderson, Aja Huang, Timo Ewalds, Martin Müller, and the referees for their feedback. We thank Martin for generously loaning the use of his computing cluster for our experiments.

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Jakub Pawlewicz

  2. Computing Science, University of Alberta, Edmonton, Canada

    Ryan B. Hayward

Authors
  1. Jakub Pawlewicz
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  2. Ryan B. Hayward
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Correspondence to Ryan B. Hayward .

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Editors and Affiliations

  1. Tilburg University, Tilburg, The Netherlands

    H. Jaap van den Herik

  2. JAIST, Ishikawa, Japan

    Hiroyuki Iida

  3. Tilburg University, Tilburg, The Netherlands

    Aske Plaat

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Pawlewicz, J., Hayward, R.B. (2014). Scalable Parallel DFPN Search. In: van den Herik, H., Iida, H., Plaat, A. (eds) Computers and Games. CG 2013. Lecture Notes in Computer Science(), vol 8427. Springer, Cham. https://doi.org/10.1007/978-3-319-09165-5_12

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  • DOI: https://doi.org/10.1007/978-3-319-09165-5_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09164-8

  • Online ISBN: 978-3-319-09165-5

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