Hierarchical Placement and Network Design Problems

In this paper, we give the rst constant-approximations for a number of layered network design problems. We begin by modeling hierarchical caching, where caches are placed in layers and each layer satis es a xed percentage of the demand (bounded miss rates). We present a constant approximation to the minimum total cost of placing the caches and routing demand through the layers. We extend this model to cover more general layered caching scenarios, giving the rst constant approximation to the well studied multi-level facility location problem. We consider a facility location variant, the Load Balanced Facility Location problem in which every demand is served by a unique facility and each open facility must serve at least a certain amount of demand. By combining Load Balanced Facility Location with our results on hierarchical caching, we give the rst constant approximation for the Access Network Design problem. Department of Computer Science, Stanford University CA 94305. Research Supported by IBM Research Fellowship, NSF Grant IIS-9811904 and NSF Award CCR-9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Email: [email protected]. Department of Computer Science, Stanford University CA 94305. Supported by ARO DAAG-55-97-1-0221. Email: [email protected]. Department of Computer Science, Stanford University CA 94305. Supported by ONR N00014-98-1-0589. Email: [email protected].