Reformulating the Dual Graphs of CSPs to Improve the Performance of Relational Neighborhood Inverse Consistency

Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a new local consistency property for binary Constraint Satisfaction Problems (CSPs). Two advantages of the algorithm for enforcing NIC is that it automatically adapts its filtering power to the local connectivity of the network and has insignificant space overhead. However, studies on binary CSPs have shown that enforcing NIC is not effective on sparse graphs and too costly on dense graphs. In (Woodward et al. 2011), we introduced an algorithm for enforcing Relational Neighborhood Inverse Consistency (RNIC), which is an extension of NIC to non-binary CSPs. In this paper, we discuss how we enhance the propagation effectiveness of our algorithm and reduce its computational cost by reformulating the dual graph of the CSP. For that purpose, we describe two reformulation techniques that modify the topology of the dual graph without affecting the solution set of the problem. We present the two reformulations and their combinations, and discuss their effects on the consistency property enforced by the algorithm. We also describe a selection policy that nicely ties together the various components of our approach in a consistent, adaptive framework. Finally, we show that our automated selection policy outperforms all approaches in a statistically significant manner

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier