Inverse 1-median problem on trees under weighted l∞norm

Authors:
Xiucui Guan;Binwu Zhang
Affiliations:
Department of Mathematics, Southeast University, Nanjing, China;Department of Mathematics and Physics, Hohai University, Changzhou, China
Venue:
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Year:
2010

Citing 4
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The Complexity Analysis of the Inverse Center Location Problem

Journal of Global Optimization
Inverse 1-center location problems with edge length augmentation on trees

Computing
The inverse 1-median problem on a cycle

Discrete Optimization
Inverse median problems

Discrete Optimization

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Abstract

The inverse 1-median problem is concerned with modifying the weights of the customers at minimum cost such that a prespecified supplier becomes the 1-median of modified location problem. We first present the model of inverse 1-median problem on trees. Then we propose two algorithms to solve the problem under weighted l∞ norm with bound constraints on modifications. Based on the approach of the unbounded case, we devise a greedy-type algorithm which runs in O(n2) time, where n is the number of vertices. Based on the property of the optimal solution, we propose an O(n log n) time algorithm using the binary search.