The inverse 1-median problem on a cycle

The inverse 1-median problem on a cycle

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Article ID: iaor2009856
Country: Netherlands
Volume: 5
Issue: 2
Start Page Number: 242
End Page Number: 253
Publication Date: May 2008
Journal: Discrete Optimization
Authors: , ,
Keywords: graphs
Abstract:

Let the graph G=(V,E) be a cycle with n+1 vertices, non-negative vertex weights and positive edge lengths. The inverse 1-median problem on a cycle consists in changing the vertex weights at minimum cost so that a prespecified vertex becomes the 1-median. All cost coefficients for increasing or decreasing the weights are assumed to be 1. We show that this problem can be formulated as a linear program with bounded variables and a special structure of the constraint matrix: the columns of the linear program can be partitioned into two classes in which they are monotonically decreasing. This allows one to solve the problem in O(n2) time.

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