Abstract
We consider a min-max version of the previously studied r-gathering problem with unit-demands. The problem we consider is a metric facility-location problem, in which each open facility must serve at least r customers, and the maximum of all the facility and connection costs should be minimized (rather than their sum). This problem is motivated by scenarios in which r customers are required for a facility to be worth opening, and the costs represent the time until the facility/connection will be available (i.e., we want to have the complete solution ready as soon as possible).
We present a 3-approximation algorithm for this problem, and prove that it cannot be approximated better (assuming P ≠ NP). Next we consider this problem with the additional natural requirement that each customer will be assigned to a nearest open facility, and present a 9-approximation algorithm. We further consider previously introduced special cases and variants, and obtain improved algorithmic and hardness results.
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Armon, A. (2008). On Min-Max r-Gatherings. In: Kaklamanis, C., Skutella, M. (eds) Approximation and Online Algorithms. WAOA 2007. Lecture Notes in Computer Science, vol 4927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77918-6_11
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DOI: https://doi.org/10.1007/978-3-540-77918-6_11
Publisher Name: Springer, Berlin, Heidelberg
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