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Revisiting restricted path consistency

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Abstract

Restricted path consistency (RPC) is a strong local consistency for binary constraints that was proposed 20 years ago and was identified as a promising alternative to arc consistency (AC) in an early experimental study of local consistencies for binary constraints. However, in contrast to other strong local consistencies such as singleton arc consistency (SAC) and max restricted path consistency (maxRPC), it has been neglected since then. In this paper we revisit RPC. First we propose RPC3, a new RPC algorithm that is very easy to implement and can be efficiently applied throughout search. Then we perform a wide experimental study of RPC3 and a light version that achieves an approximation of RPC, comparing them to state-of-the-art AC and maxRPC algorithms. Experimental results obtained under various solver settings, regarding the branching scheme, the variable ordering heuristic, and restarts, clearly show that light RPC is by far more efficient than both AC and maxRPC when applied throughout search. We also examine the experimental behaviour of an algorithm for a simple extension of RCP called 2-RPC, showing that it is competitive with RPC3, and better than both AC and maxRPC. Overall, our results strongly suggest that it is time to reconsider the established perception that MAC is the best general purpose method for solving binary CSPs.

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Notes

  1. This holds under a d-way branching scheme. Under binary branching it will be also called after a value removal.

  2. This version of RPC3 was called restricted RPC3 in [27].

  3. We follow the usual assumption that a binary constraint check takes constant time.

  4. Data points from the easy ehi class are not included in these plots.

  5. d-way branching was employed in these experiments.

  6. In fact, AC takes 3370 seconds on this instance (i.e. close to the cut-off limit), while lRPC takes 4086. Therefore, the difference is not very significant.

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Correspondence to Kostas Stergiou.

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This is an extended version of a short CP-2015 paper [27].

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Stergiou, K. Revisiting restricted path consistency. Constraints 22, 377–402 (2017). https://doi.org/10.1007/s10601-016-9255-9

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