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- W4205841297 abstract "We examine the Online Facility Location problem in an extended version. Fotakis showed a lower bound of Ω(lognloglogn) for the original Online Facility Location problem, where n is the number of clients. This bound holds even on the real line and for randomized algorithms against oblivious adversaries. We propose randomized online algorithms in the following setting: We consider the Euclidean space of arbitrary dimension and allow the facilities to either move arbitrarily or to move at most a constant distance m in each time step. The costs for moving a facility from a to b is D⋅d(a,b) where D≥1 is a constant. Clients are assigned to facilities instantly and irreversibly. The cost for serving the clients is either calculated as soon as a client arrives or at the end of the computation. The algorithms for these two cost models achieve the same competitiveness on the line, which, in contrast to the original Online Facility Location problem, is independent of n. In the case of arbitrary movement, it only depends on D. In the case of a limited movement distance m, it additionally depends on m and the opening costs of the facilities. We show that our results are asymptotically tight on the real line. For the Euclidean space of higher dimensions, we give an algorithm for the model where costs for clients are evaluated immediately. The competitive ratio of our algorithm depends on the above parameters and additionally on the number of optimal facilities." @default.
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- W4205841297 date "2022-03-01" @default.
- W4205841297 modified "2023-10-13" @default.
- W4205841297 title "Online facility location with mobile facilities" @default.
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- W4205841297 doi "https://doi.org/10.1016/j.tcs.2022.01.019" @default.
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