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Mathematical Problems in Engineering
Volume 2013, Article ID 313868, 6 pages
http://dx.doi.org/10.1155/2013/313868
Research Article

The Inverse 1-Median Problem on Tree Networks with Variable Real Edge Lengths

1College of Science, China Jiliang University, Hangzhou 310018, China
2Division of Computer Science and Engineering, Chonbuk National University, Jeonju, Jeonbuk 561-756, Republic of Korea
3College of Computer Science, Zhejiang University of Technology, Hangzhou 310023, China

Received 25 January 2013; Accepted 22 March 2013

Academic Editor: Carlo Cattani

Copyright © 2013 Longshu Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Location problems exist in the real world and they mainly deal with finding optimal locations for facilities in a network, such as net servers, hospitals, and shopping centers. The inverse location problem is also often met in practice and has been intensively investigated in the literature. As a typical inverse location problem, the inverse 1-median problem on tree networks with variable real edge lengths is discussed in this paper, which is to modify the edge lengths at minimum total cost such that a given vertex becomes a 1-median of the tree network with respect to the new edge lengths. First, this problem is shown to be solvable in linear time with variable nonnegative edge lengths. For the case when negative edge lengths are allowable, the NP-hardness is proved under Hamming distance, and strongly polynomial time algorithms are presented under and norms, respectively.