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International Conference on Principles and Practice of Constraint Programming

CP 1995: Principles and Practice of Constraint Programming — CP '95 pp 70–87Cite as

Scaling effects in the CSP phase transition

  • Constraint Satisfaction Problems 1
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 976))

Abstract

Phase transitions in constraint satisfaction problems (CSP's) are the subject of intense study. We identify a control parameter for random binary CSP's. There is a rapid transition in the probability of a CSP having a solution at a critical value of this parameter. This parameter allows different phase transition behaviour to be compared in an uniform manner, for example CSP's generated under different regimes. We then show that within classes, the scaling of behaviour can be modelled by a technique called “finite size scaling”. This applies not only to probability of solubility, as has been observed before in other NP-problems, but also to search cost. Furthermore, the technique applies with equal validity to several different methods of varying problem size. As well as contributing to the understanding of phase transitions, we contribute by allowing much finer grained comparison of algorithms, and for accurate empirical extrapolations of behaviour.

The fourth author is supported by an HCM Postdoctoral Fellowship. We thank the Department of Computer Science at the University of Strathclyde for CPU cycles, and Judith Underwood for her help.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Strathclyde, G1 1XH, Glasgow, UK

    Ian P. Gent, Ewan MacIntyre & Patrick Prosser

  2. Mechanized Reasoning Group, IRST, Trento

    Toby Walsh

  3. DIST, University of Genoa, Italy

    Toby Walsh

Authors
  1. Ian P. Gent
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  2. Ewan MacIntyre
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  3. Patrick Prosser
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  4. Toby Walsh
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Editor information

Ugo Montanari Francesca Rossi

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© 1995 Springer-Verlag Berlin Heidelberg

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Gent, I.P., MacIntyre, E., Prosser, P., Walsh, T. (1995). Scaling effects in the CSP phase transition. In: Montanari, U., Rossi, F. (eds) Principles and Practice of Constraint Programming — CP '95. CP 1995. Lecture Notes in Computer Science, vol 976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60299-2_5

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  • DOI: https://doi.org/10.1007/3-540-60299-2_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60299-6

  • Online ISBN: 978-3-540-44788-7

  • eBook Packages: Springer Book Archive

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