Reformulating CSPs for Scalability with Application to Geospatial Reasoning

Abstract

While many real-world combinatorial problems can be advantageously modeled and solved using Constraint Programming, scalability remains a major issue in practice. Constraint models that accurately reflect the inherent structure of a problem, solvers that exploit the properties of this structure, and reformulation techniques that modify the problem encoding to reduce the cost of problem solving are typically used to overcome the complexity barrier. In this paper, we investigate such approaches in a geospatial reasoning task, the building-identification problem (BID), introduced and modeled as a Constraint Satisfaction Problem by Michalowski and Knoblock [1]. We introduce an improved constraint model, a custom solver for this problem, and a number of reformulation techniques that modify various aspects of the problem encoding to improve scalability. We show how interleaving these reformulations with the various stages of the solver allows us to solve much larger BID problems than was previously possible. Importantly, we describe the usefulness of our reformulations techniques for general Constraint Satisfaction Problems, beyond the BID application.