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 ik and ensures that i is open for the next l k time steps. In addition to costs for opening facilities, we have to take connection 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 [7] and is strongly related to both the online facility problem by [5] and the parking permit problem by [6]. Nagarajan and Williamson gave a 3-approximation algorithm for the offline problem and an O(Klogn)-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 algorithm is O(l maxlog(l max))-competitive. Here denotes the maximum lease length. Moreover, we prove that it is -competitive for many "natural" 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 polynomially bounded in l max. © 2012 Springer-Verlag.
CITATION STYLE
Kling, P., Meyer Auf Der Heide, F., & Pietrzyk, P. (2012). An algorithm for online facility leasing. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7355 LNCS, pp. 61–72). https://doi.org/10.1007/978-3-642-31104-8_6
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