On Combinatorial Optimization Problems with Mobile Sites and Resources

This paper develops a framework to solve combinatorial resource allocation problems in a setting where the sites and resources are allowed to have dynamics. The formulation draws analogy from statistical physics to define the Free Energy function which is used as a measure of coverage function. A class of dynamics for the sites and resources is prescribed which guarantees coverage. This is done by casting the problem as a control problem in which we design the resource velocities to ensure that the time derivative of the Free Energy function is non positive.