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

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2010

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Hatzl, Johannes

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http://nbn-resolving.de/urn:nbn:de:bsz:352-126362
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https://doi.org/10.1016/j.orl.2010.07.002
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Informatik und Informationswissenschaft: Publikationen
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Operations Research Letters. 2010, 38(5), pp. 383-385. ISSN 0167-6377. Available under: doi: 10.1016/j.orl.2010.07.002

Zusammenfassung

We consider the 1-median problem in Rd the MathML source 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.

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004 Informatik

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Facility location, 1-median problem, Fractional b-matching

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ISO 690HATZL, Johannes, Andreas KARRENBAUER, 2010. A combinatorial algorithm for the 1-median problem in Rd with the Chebyshev norm. In: Operations Research Letters. 2010, 38(5), pp. 383-385. ISSN 0167-6377. Available under: doi: 10.1016/j.orl.2010.07.002
BibTex
@article{Hatzl2010combi-12636,
  year={2010},
  doi={10.1016/j.orl.2010.07.002},
  title={A combinatorial algorithm for the 1-median problem in Rd with the Chebyshev norm},
  number={5},
  volume={38},
  issn={0167-6377},
  journal={Operations Research Letters},
  pages={383--385},
  author={Hatzl, Johannes and Karrenbauer, Andreas}
}
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