A Competitive, Primal-Dual Algorithm for Stable Coalitions in a Cluster

In this paper we study the following Cluster Profit Problem. Highly parallelizable requests arrive on network nodes. Each request is associated with a tuple (g, r). The requester is willing to pay kg if k machines execute the request in parallel. If some machines work on a request, the machines must pay the request processing costs, r, as well as connection costs to the request. The problem is to find a profit maximizing assignment of machines to request, such that each machine works on at most one request. The Cluster Profit Problem can be viewed as a profit maximizing variant of the Facility Location Problem. We show a constant-competitive, primal-dual algorithm for the Cluster Profit Problem. We show the algorithm is game theoretically stable with respect to group deviations on the part of the participating machines. Finally, we provide a distributed implementation of the algorithm that uses only local network structure for the required computations.