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New Algorithms for Facility Location Problems on the Real Line

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Abstract

In this paper, we study the facility location problems on the real line. Given a set of n customers on the real line, each customer having a cost for setting up a facility at its position, and an integer k, we seek to find at most k of the customers to set up facilities for serving all n customers such that the total cost for facility set-up and service transportation is minimized. We consider several problem variations including the k-median, the k-coverage, and the linear model. The previously best algorithms for these problems all take O(nk) time. Our new algorithms break the O(nk) time bottleneck and solve these problems in sub-quadratic time. Our algorithms are based on a new problem modeling and interesting algorithmic techniques, which may find other applications as well.

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Acknowledgement

The research of Chen was supported in part by NSF under Grants CCF-0916606 and CCF-1217906.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Danny Z. Chen

  2. Department of Computer Science, Utah State University, Logan, UT, 84322, USA

    Haitao Wang

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  1. Danny Z. Chen
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  2. Haitao Wang
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Correspondence to Haitao Wang.

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Chen, D.Z., Wang, H. New Algorithms for Facility Location Problems on the Real Line. Algorithmica 69, 370–383 (2014). https://doi.org/10.1007/s00453-012-9737-0

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