Brief Announcement: Approximation Algorithms for Unsplittable Resource Allocation Problems with Diseconomies of Scale

We study general resource allocation problems with a diseconomy of scale. Given a finite set of commodities that request certain resources, the cost of each resource grows superlinearly with the demand for it, and our goal is to minimize the total cost of the resources. In large systems with limited coordination, it is natural to consider local dynamics where in each step a single commodity switches its allocated resources whenever the new solution after the switch has smaller total cost over all commodities. This yields a deterministic and polynomial time algorithm with approximation factor arbitrarily close to the locality gap, i.e., the worst case ratio of the cost of a local optimal and a global optimal solution. For costs that are polynomials with non-negative coefficients and maximal degree d, we provide a locality gap for weighted problems that is tight for all values of d. For unweighted problems, the locality gap asymptotically matches the approximation guarantee of the currently best known centralized algorithm [Makarychev, Srividenko FOCS14] but only requires local knowledge of the commodities.