Revisiting the efficacy of weak consistencies:a study of forward checking

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Dear editor,rnArc consistency(AC)[1]is currently the most popular lo-cal consistency for solving constraint satisfaction problems(CSP).To solve CSPs more efficiently,extensive work[2-4]has been done to find local consistencies that perform better than AC.Efforts have primarily been focused on consisten-cies that are stronger than AC.Even though a stronger con-sistency is able to eliminate more inconsistent values than AC,enforcing a stronger consistency is more expensive.It is never easy to determine the optimal tradeoff between a consistency\'s pruning ability and its propagation cost.In recent years,numerous stronger local consistencies,such as max-restricted path consistency(maxRPC)[2],partition-one-ac(POAC)[3],neighborhood singleton arc consistency(NSAC)and restricted NSAC(RNSAC)[4]have been shown to be competitive with AC.These stronger consistencies have been shown to outperform AC on a number of prob-lems.
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