Inverse median problems

Authors:
Rainer E. Burkard;Carmen Pleschiutschnig;Jianzhong Zhang
Affiliations:
Institute of Optimization, Dynamical Systems and Discrete Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria;Institute of Optimization, Dynamical Systems and Discrete Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria;Department of Mathematics, City University of Hong Kong, Hong Kong
Venue:
Discrete Optimization
Year:
2004

Citing 4
Cited 7

On an instance of the inverse shortest paths problem

Mathematical Programming: Series A and B
Improving the location of minisum facilities through network modification

Annals of Operations Research - Special issue on locational decisions
The Complexity Analysis of the Inverse Center Location Problem

Journal of Global Optimization
A Survey on Obnoxious Facility Location Problems

A Survey on Obnoxious Facility Location Problems

Reverse 2-median problem on trees

Discrete Applied Mathematics
Inverse 1-center location problems with edge length augmentation on trees

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

AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Uniform-cost inverse absolute and vertex center location problems with edge length variations on trees

Discrete Applied Mathematics
An inverse approach to convex ordered median problems in trees

Journal of Combinatorial Optimization
A combinatorial algorithm for the 1-median problem in Rd with the Chebyshev norm

Operations Research Letters
The inverse 1-median problem on a cycle

Discrete Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

The inverse p-median problem consists in changing the weights of the customers of a p-median location problem at minimum cost such that a set of p prespecified suppliers becomes the p-median. The cost is proportional to the increase or decrease of the corresponding weight. We show that the discrete version of an inverse p-median problem can be formulated as a linear program. Therefore, it is polynomially solvable for fixed p even in the case of mixed positive and negative customer weights. In the case of trees with nonnegative vertex weights, the inverse 1-median problem is solvable in a greedy-like fashion. In the plane, the inverse 1-median problem can be solved in O(nlogn) time, provided the distances are measured in l"1- or l"~-norm, but this is not any more true in R^3 endowed with the Manhattan metric.