Inverse 1-median problem on trees under weighted Hamming distance

Listed:
• Xiucui Guan

()

• Binwu Zhang

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

Suggested Citation

• Xiucui Guan & Binwu Zhang, 2012. "Inverse 1-median problem on trees under weighted Hamming distance," Journal of Global Optimization, Springer, vol. 54(1), pages 75-82, September.
• Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:75-82
DOI: 10.1007/s10898-011-9742-x
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File URL: http://hdl.handle.net/10.1007/s10898-011-9742-x

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References listed on IDEAS

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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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Cited by:

1. Nguyen, Kien Trung & Chassein, André, 2015. "The inverse convex ordered 1-median problem on trees under Chebyshev norm and Hamming distance," European Journal of Operational Research, Elsevier, vol. 247(3), pages 774-781.
2. repec:spr:joptap:v:178:y:2018:i:2:d:10.1007_s10957-018-1221-9 is not listed on IDEAS

Keywords

Inverse 1-median problem; Tree; Weighted Hamming distance; Binary search; 0-1 knapsack problem;

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