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International Conference on Agents and Artificial Intelligence

ICAART 2019: Agents and Artificial Intelligence pp 72–99Cite as

Social Golfer Problem Revisited

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11978))

Abstract

In a golf club, \(n=g*s\) golfers want to play in g groups of s golfers for w weeks. Does there exist a schedule for each golfer to play no more than once with any other golfer? This simple but overwhelmingly challenging problem, which is called social golfer problem (SGP), has received considerable attention in constraint satisfaction problem (CSP) research as a standard benchmark for symmetry breaking. However, constraint satisfaction approach for solving the SGP has stagnated in terms of larger instance over the last decade. In this article, we improve the existing model of the SGP by introducing more constraints that effectively reduce the search space, particularly for the instances of the specific form. And on this basis, we also provide a search space splitting method to solve the SGP in parallel via data-level parallelism. Our implementation of the presented techniques allows us to attain the solutions for eight instances with maximal number of weeks, in which six of them were open instances for constraint satisfaction approach, and two of them are computed for the first time, and super-linear speedups are observed for all the instances solved in parallel. Besides, we survey the extensive literature on solving the SGP, including the best results they have achieved, and analyse the cause of difficulties in solving the SGP.

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Notes

  1. 1.

    This article follows the naming convention and order of the arguments of constraints in Choco solver.

  2. 2.

    In this article, we follow the Zero-based index.

  3. 3.

    The % (modulo) operator yields the remainder from the division of the first operand by the second.

  4. 4.

    Two Latin squares are mutually orthogonal if, they have the same order n and when superimposed, each of the possible \(n^2\) ordered pairs occur exactly once.

  5. 5.

    An affine plane of order n exists iff a projective plane of order n exists.

  6. 6.

    For instance, \(14=2*7\equiv ~2~(\text {mod}\ 4)\), and the primes in the square-free part are 2 and 7.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science (MINT), Brandenburg University of Technology Cottbus-Senftenberg, Konrad-Wachsmann-Allee 5, 03044, Cottbus, Germany

    Ke Liu, Sven Löffler & Petra Hofstedt

Authors
  1. Ke Liu
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  2. Sven Löffler
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  3. Petra Hofstedt
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Corresponding author

Correspondence to Ke Liu .

Editor information

Editors and Affiliations

  1. Leiden University, Leiden, The Netherlands

    Jaap van den Herik

  2. LIACC, University of Porto, Porto, Portugal

    Ana Paula Rocha

  3. ICREA, Institute of Evolutionary Biology, Barcelona, Spain

    Luc Steels

Appendices

A Appendix

The Solutions

See Tables 11, 12, 13, 14, 15, 16 and 17.

Table 11. The solution for 6-3-8 transformed from the solution shown in Table 6.
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Table 12. A new non-isomorphic solution for the 6-3-8 instance.
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Table 13. The solution for 6-4-7 transformed from the solution shown in Table 7.
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Table 14. A new non-isomorphic solution for the 7-3-10 instance.
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Table 15. A new non-isomorphic solution for the 7-3-10 instance.
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Table 16. A new non-isomorphic solution for the 7-3-10 instance.
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Table 17. A solution of 8-8-9 expressed by groups.
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Liu, K., Löffler, S., Hofstedt, P. (2019). Social Golfer Problem Revisited. In: van den Herik, J., Rocha, A., Steels, L. (eds) Agents and Artificial Intelligence. ICAART 2019. Lecture Notes in Computer Science(), vol 11978. Springer, Cham. https://doi.org/10.1007/978-3-030-37494-5_5

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  • DOI: https://doi.org/10.1007/978-3-030-37494-5_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-37493-8

  • Online ISBN: 978-3-030-37494-5

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