A combinatorial algorithm for the 1-median problem in Rd with the Chebyshev norm

Authors:
Johannes Hatzl;Andreas Karrenbauer
Affiliations:
Department of Optimization and Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria;Department of Computer and Information Science, Zukunftskolleg, University of Konstanz, Box 216, 78457 Konstanz, Germany
Venue:
Operations Research Letters
Year:
2010

Citing 3
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Abstract

We consider the 1-median problem in R^d with the Chebyshev norm: given n points with non-negative weights, find a point that minimizes the sum of the weighted distances to the given points. We propose a combinatorial algorithm for this problem by reformulating it as a fractional b-matching problem. This graph-theoretical problem can be solved by a min-cost-flow algorithm. Moreover, we show that there is a 1-median, which is half-integral, provided that the points have integral coordinates.