Domain Filtering Consistencies

Abstract

Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms of arc consistency have been widely studied, and have been known for sometime through the forward checking or the MAC search algorithms. Until recently, stronger forms of local consistency remained limited to those that change the structure of the constraint graph, and thus, could not be used in practice, especially on large networks. This paper focuses on the local consistencies that are stronger than arc consistency, without changing the structure of the network, i.e., only removing inconsistent values from the domains. In the last five years, several such local consistencies have been proposed by us or by others. We make an overview of all of them, and highlight some relations between them. We compare them both theoretically and experimentally, considering their pruning efficiency and the time required to enforce them.

Revisiting Neighborhood Inverse Consistency on Binary CSPs

“…Further, Lecoutre et al show that, on binary CSPs, strong Conservative Dual Consistency (sCDC) is equal SAC+CDC [14]. 5 While NIC was shown to be incomparable to SAC [5], its relationship to sCDC has not yet been addressed [13]. In this paper, we complete the comparison of NIC, RNIC, and sCDC, and show that they are, both theoretically and empirically, pairwise incomparable.…”

“…Strong consistency properties for binary CSPs that do not affect the topology of the constraint graph have been carefully reviewed, studied, and compared to each others [5,14]. Such properties include maxRPC [3], SAC [4], CDC [13], and, the strongest of them all, sCDC [14].…”

“…variables domains. In Figure 10, borrowed from Debruyne and Bessière [5], the CSP is sCDC but not RNIC+DF. RNIC removes {(2, 3), (3, 2)} from R 2 , {(1, 2), (1, 3)} from R 1 , and {(1, 2), (1, 3)} from R 5 .…”

“…Proof: In Figure 9, the CSP is NIC but not sCDC. In Figure 11, borrowed from Debruyne and Bessière [5], the CSP is sCDC but not NIC. NIC removes the value 1 from A.…”

“…Freuder and Elfe tested their algorithm in a preprocessing step to backtrack search for solving binary instances whose constraint density did not exceed 4.25% [8]. Debruyne and Bessière showed that NIC is ineffective on sparse graphs and too costly on dense graphs [5].…”