Abstract
We show that the same methodology used to study phase transition behaviour in NP-complete problems works with a polynomial problem class: establishing arc consistency. A general measure of the constrainedness of an ensemble of problems, used to locate phase transitions in random NP-complete problems, predicts the location of a phase transition in establishing arc consistency. A complexity peak for the AC3 algorithm is associated with this transition. Finite size scaling models both the scaling of this transition and the computational cost. On problems at the phase transition, this model of computational cost agrees with the theoretical worst case. As with NP-complete problems, constrainedness — and proxies for it which are cheaper to compute — can be used as a heuristic for reducing the number of checks needed to establish arc consistency in AC3.
The authors are supported by EPSRC awards GR/L/24014 and GR/K/65706, and the EU award EU20603. The authors wish to thank other members of the APES research group for their help, and Gene Freuder.
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© 1997 Springer-Verlag Berlin Heidelberg
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Gent, I.P., MacIntyre, E., Prosser, P., Shaw, P., Walsh, T. (1997). The constrainedness of Arc consistency. In: Smolka, G. (eds) Principles and Practice of Constraint Programming-CP97. CP 1997. Lecture Notes in Computer Science, vol 1330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017449
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DOI: https://doi.org/10.1007/BFb0017449
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