Distributed problem solving in geometrically-structured constraint networks

Abstract

Distributed Constraint Satisfaction (DisCSP) is a popular formalism that is used for developing a wide variety of general-purpose protocols. With very few exceptions, these protocol are tested using completely random instances with the understanding that this leads to better overall solutions. In many real-world situations, however, the variables in the problem represent objects that exist in n-dimensional space with constraints between them based on distance. In such instances, the constraint network forms a geometric graph and therefore is referred to as a Geometrically-Structured Constraint Satisfaction Problem (GS-CSP). This paper introduces the GS-CSP and evaluates the performance of two complete DisCSP protocols to demonstrate how the introduction of structure affects these general problem solving approaches. Our findings show that GS-CSPs possess unique characteristics particularly in the phase transition regions and these characteristics can have a dramatic impact on the performance of current DisCSP algorithms.