Shant Karakashian

Revisiting Neighborhood Inverse Consistency on Binary CSPs

Our goal is to investigate the definition and application of strong consistency properties on the dual graphs of binary Constraint Satisfaction Problems (CSPs). As a first step in that direction, we study the structure of the dual graph of binary CSPs, and show how it can be arranged in a triangle-shaped grid. We then study, in this context, Relational Neighborhood Inverse Consistency (RNIC), which is a consistency property that we had introduced for non-binary CSPs [17]. We discuss how the structure of the dual graph of binary CSPs affects the consistency level enforced by RNIC. Then, we compare, both theoretically and empirically, RNIC to Neighborhood Inverse Consistency (NIC) and strong Conservative Dual Consistency (sCDC), which are higher-level consistency properties useful for solving difficult problem instances. We show that all three properties are pairwise incomparable.

Relational consistency by constraint filtering

In this paper, we propose a new algorithm for enforcing relational consistency on every set of k constraints of a finite Constraint Satisfaction Problem (CSP). This algorithm operates by filtering the constraint while leaving the topology of the graph unchanged. We study the resulting relational consistency property and compare it to existing ones. We evaluate the effectiveness of our algorithm in a search procedure for solving CSPs and demonstrate the applicability, effectiveness, and usefulness of enforcing high levels of consistency.