# Inverse 1-median problem on trees under weighted Hamming distance

## Author Info

• Xiucui Guan

()

• Binwu Zhang
Registered author(s):

## Abstract

The inverse 1-median problem consists in modifying the weights of the customers at minimum cost such that a prespecified supplier becomes the 1-median of modified location problem. A linear time algorithm is first proposed for the inverse problem under weighted l ∞ norm. Then two polynomial time algorithms with time complexities O(n log n) and O(n) are given for the problem under weighted bottleneck-Hamming distance, where n is the number of vertices. Finally, the problem under weighted sum-Hamming distance is shown to be equivalent to a 0-1 knapsack problem, and hence is $${\mathcal{NP}}$$ -hard. Copyright Springer Science+Business Media, LLC. 2012

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File URL: http://hdl.handle.net/10.1007/s10898-011-9742-x

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## Bibliographic Info

Article provided by Springer in its journal Journal of Global Optimization.

Volume (Year): 54 (2012)
Issue (Month): 1 (September)
Pages: 75-82

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 Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:75-82 Contact details of provider: Web page: http://www.springer.com/business/operations+research/journal/10898 Order Information: Web: http://link.springer.de/orders.htm

## References

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1. Burkard, Rainer E. & Galavii, Mohammadreza & Gassner, Elisabeth, 2010. "The inverse Fermat-Weber problem," European Journal of Operational Research, Elsevier, vol. 206(1), pages 11-17, October.
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