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A linear programming approach to increasing the weight of all minimum spanning trees
Author(s) -
Baïou Mourad,
Barahona Francisco
Publication year - 2008
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20242
Subject(s) - linear programming , piecewise linear function , mathematics , minimum spanning tree , minimum weight , spanning tree , mathematical optimization , combinatorics , regular polygon , graph , geometry
Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. Frederickson and Solis‐Oba gave an algorithm for the case when the costs are linear. We give a different derivation of their algorithm, and we slightly extend it to deal with convex piecewise linear costs. We formulate the problem as a combinatorial linear program and show how to produce primal and dual solutions. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008