@inproceedings{636,
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 lk. Opening a facility i using lease type k causes a cost of f k i and ensures that i is open for the next lk time steps. In addition to costs for opening facilities, we have to take connection costs ci j 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 Nagarajan 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(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(lmax log(lmax))-competitive. Here lmax denotes the maximum lease length. Moreover, we prove that it is O(log2(lmax))-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 lmax.},
author = {Meyer auf der Heide, Friedhelm and Pietrzyk, Peter and Kling, Peter},
booktitle = {Proceedings of the 19th International Colloquium on Structural Information & Communication Complexity (SIROCCO)},
pages = {61--72},
title = {{An Algorithm for Facility Leasing}},
doi = {10.1007/978-3-642-31104-8_6},
year = {2012},
}