Fast distributed scheduling via primal-dual

Alessandro Panconesi, Mauro Sozio

Abstract: In this paper we give an efficient distributed algorithm computing approximate solutions to a very general, and classical, scheduling problem. The approximation guarantee is within a constant factor of the optimum. By "efficient", we mean that the number of communication rounds is poly-logarithmic in the size of the input. In the problem, we have a bipartite graph with computing agents on one side and resources on the other. Agents that share a resource can communicate in one time step. Each agent has a list of jobs, each with its own length and profit, to be executed on a neighbouring resource within a given time-window. Resources can execute non preemptively only one job at a time. The goal is to maximize the profit of the jobs that are scheduled. It is well known that this problem is NP-hard. A very interesting feature of our algorithm is that it is derived in a systematic manner from a primal-dual algorithm.