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\(k\)-center problems with minimum coverage. (English) Zbl 1070.68155

Summary: We study an extension of the \(k\)-center facility location problem, where centers are required to service a minimum of clients. This problem is motivated by requirements to balance the workload of centers while allowing each center to cater to a spread of clients. We study three variants of this problem, all of which are shown to be NP-hard. In-approximation hardness and approximation algorithms with factors equal or close to the best lower bounds are provided. Generalizations, including vertex costs and vertex weights, are also studied.

MSC:

68W25 Approximation algorithms
90B80 Discrete location and assignment
90C59 Approximation methods and heuristics in mathematical programming
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