We consider the mobile facility location (MFL) problem. We are given a set of facilities and clients located in a common metric space G = (V, c). The goal is to move each facility from its initial location to a destination (in V ) and assign each client to the destination of some facility so as to minimize the sum of the movement-costs of the facilities and the client-assignment costs. This abstracts facility-location settings where one has the flexibility of moving facilities from their current locations to other destinations so as to serve clients more efficiently by reducing their assignment costs. We give the first local-search based approximation algorithm for this problem and achieve the bestknown approximation guarantee. Our main result is (3 + )-approximation for this problem for any constant > 0 using local search. The previous best guarantee for MFL was an 8-approximation algorithm due to [13] based on LP-rounding. Our guarantee matches the best-known approximation guarantee for the k-median problem. Since there is an approximation-preserving reduction from the k-median problem to MFL, any improvement of our result would imply an analogous improvement for the k-median problem. Furthermore, our analysis is tight (up to o(1) factors) since the tight example for the local-search based 3-approximation algorithm for k-median can be easily adapted to show that our local-search algorithm has a tight approximation ratio of 3. One of the chief novelties of the analysis is that in order to generate a suitable collection of local-search moves whose resulting inequalities yield the desired bound on the cost of a local-optimum, we define a tree-like structure that (loosely speaking) functions as a "recursion tree", using which we spawn off local-search moves by exploring this tree to a constant depth. Our results extend to the weighted generalization wherein each facility i has a non-negative weight w i and the movement cost for i is w i times the distance traveled by i.
A polynomial (3 + )-approximation algorithm was shown in REF .
Local-Search based Approximation Algorithms for Mobile Facility Location Problems
ArXiv
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Mathematics Computer Science