The Phase Transition in Distributed Constraint Satisfaction Problems: Fist Results

We examine the behavior of a distributed constraint satisfaction algorithm. More specifically, we measured the communication and computation costs of a distributed constraint satisfaction algorithm when varying the numbers of intra-agent constraints (constraints which are defined over variables of one agent) and inter-agent constraints (constraints which are defined over variables of multiple agents) for distributed graph 3-coloring problems. What we found from our experiments are: 1) the phase transition occurs in the narrow region on the x-y plane (where the x-axis is the number of intra-agent constraints and the y-axis is the number of inter-agent constraints), where the sum of intraand inter-agent constraints is constant, and problems in the phase transition region are likely to be expensive in terms of the median communication and computation costs; 2) among problems in the phase transition region, problems with a smaller number of intra-agent constraints and a larger number of inter-agent constraints can be more expensive; 3) for a fixed total number of variables, problems in the phase transition region can be more expensive as the number of agents increases or the number of variables per agent decreases.