A natural model and a parallel algorithm for approximately solving the maximum weighted independent set problem

A dynamical model based upon a physical metaphor is described, and a parallel algorithm inspired from the model is developed for approximately solving maximum weight independent set problem. Our model treats an independent set as an attraction game, where vertices of the graph are considered as still bodies and edges as cells attracted by the still bodies corresponding to its extremities. In addition, we discuss how, by using an analogous model, an approximation algorithm can be developed for the minimum set covering problem.