FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A primal-dual algorithm for online non-uniform facility location
Journal of Discrete Algorithms
Infrastructure Leasing Problems
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Offline and online facility leasing
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Parallel approximation algorithms for facility-location problems
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Rapid randomized pruning for fast greedy distributed algorithms
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
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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 $f_i^k$ 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 cij 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 $O (\ensuremath{l_{\text{max}}} \log(\ensuremath{l_{\text{max}}}))$-competitive. Here $\ensuremath{l_{\text{max}}} $ denotes the maximum lease length. Moreover, we prove that it is $O (\log^2(\ensuremath{l_{\text{max}}}))$-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 $l_{\text{max}}$.