New approximation algorithms for the unsplittable capacitated facility location problem

• Authors: Babak Behsaz;Mohammad R. Salavatipour;Zoya Svitkina
• Venue: SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
• Year: 2012

In this paper, we consider the Unsplittable (hard) Capacitated Facility Location Problem (UCFLP) with uniform capacities and present some new approximation algorithms for it. This problem is a generalization of the classical facility location problem where each facility can serve at most u units of demand and each client must be served by exactly one facility. It is known that it is NP-hard to approximate this problem within any factor without violating the capacities. So we consider bicriteria (α,β)-approximations where the algorithm returns a solution whose cost is within factor α of the optimum and violates the capacity constraints within factor β. We present a framework for designing bicriteria approximation algorithms and show two new approximation algorithms with factors (10.173,3/2) and (30.432,4/3). These are the first algorithms with constant approximation in which the violation of capacities is below 2. The heart of our algorithms is a reduction from the UCFLP to a restricted version of the problem. One feature of this reduction is that any (O(1),1+ε)-approximation for the restricted version implies an (O(1),1+ε)-approximation for the UCFLP for any constant ε0 and we believe our techniques might be useful towards finding such approximations or perhaps (f(ε),1+ε)-approximation for the UCFLP for some function f. In addition, we present a quasi-polynomial time (1+ε,1+ε)-approximation for the (uniform) UCFLP in Euclidean metrics, for any constant ε0.