An Algorithm for Online Facility Leasing ⋆ Peter Kling, Friedhelm Meyer auf der Heide, and Peter Pietrzyk Heinz Nixdorf Institute & Computer Science Department, University of Paderborn, 33095 Paderborn, Germany {peter.kling,fmadh,peter.pietrzyk}@upb.de Abstract. We consider an online facility location problem where clients arrive over time and their demands have to be served by opening facilities and assigning the clients to opened facilities. When opening a facility we must choose one of K different lease types to use. A lease type k has a certain lease length l k . Opening a facility i using lease type k causes a cost of f k i and ensures that i is open for the next l k time steps. In addition to costs for opening facilities, we have to take con- nection costs c ij into account when assigning a client j to facility i. We develop and analyze the first online algorithm for this problem that has a time-independent competitive factor. This variant of the online facility location problem was introduced by Na- garajan and Williamson [7] and is strongly related to both the online facility problem by Meyerson [5] and the parking permit problem by Meyerson [6]. Nagarajan and Williamson gave a 3-approximation algorithm for the offline problem and an O(K log n)-competitive algorithm for the online variant. Here, n denotes the total number of clients arriving over time. We extend their result by removing the dependency on n (and thereby on the time). In general, our al- gorithm is O(l max log(l max ))-competitive. Here l max denotes the maximum lease length. Moreover, we prove that it is O(log 2 (l max ))-competitive for many “natu- ral” cases. Such cases include, for example, situations where the number of clients arriving in each time step does not vary too much, or is non-increasing, or is poly- nomially bounded in l max . 1 Introduction Consider a company that runs a distributed service on a network. In order to provide this service, the company has to choose a set of nodes to become service providers in such a way that they can be easily accessed by customer nodes. The nodes in the network do not belong to the company and thus have to be leased before they can be used to provide a service. There are various leases of different costs and durations. Once a lease expires, the node no longer is able to provide the service. In order to use the node again a new lease must be bought. The customer nodes can freely use any node’s service as long as there is an active lease for this node. The costs of using it are proportional to the distance (latency) between customer node and service-providing ⋆ This work was partially supported by the German Research Foundation (DFG) within the Col- laborative Research Center “On-The-Fly Computing” (SFB 901) and by the Graduate School on Applied Network Science (GSANS). G. Even and M.M. Halld´ orsson (Eds.): SIROCCO 2012, LNCS 7355, pp. 61–72, 2012. c  Springer-Verlag Berlin Heidelberg 2012