Offline and online facility leasing

Abstract

We study the problem of leasing facilities over time, following the general infrastructure leasing problem framework introduced by Anthony and Gupta (2007). If there are K different lease types, Anthony and Gupta give an O(K)-approximation algorithm for the problem. We are able to improve this to a 3-approximation algorithm by using a variant of the primal–dual facility location algorithm of Jain and Vazirani (2001).We also consider the online version of the facility leasing problem, in which the clients to be served arrive over time and are not known in advance. This problem generalizes both the online facility location problem (introduced by Meyerson, 2001) and the parking permit problem (also introduced by Meyerson, 2005). We give a deterministic algorithm for the problem that is O(Klogn)-competitive. No previous result was known for this problem. To achieve our result, we modify an O(logn)-competitive algorithm of Fotakis (2007) for the online facility location problem. We also reanalyze his algorithm via the dual-fitting technique to prove that it achieves the O(logn) competitive ratio.