Abstract
This paper considers the inverse 1-center location problem with edge length augmentation on a tree network T with n + 1 vertices. The goal is to increase the edge lengths at minimum total cost subject to given modification bounds such that a predetermined vertex s becomes an absolute 1-center under the new edge lengths. Using a set of suitably extended AVL-search trees we develop a combinatorial algorithm which solves the inverse 1-center location problem with edge length augmentation in O(n log n) time. Moreover, it is shown that the problem can be solved in O(n) time if all the cost coefficients are equal.
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Communicated by R. Weismantel.
B. Alizadeh acknowledges financial support by the NAWI-Project in joint cooperation between Graz University of Technology and Karl-Franzens University of Graz under the grant F-NW-MATH-05. This research has also been supported by the Austrian Science Fund (FWF) Project P18918-N18.
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Alizadeh, B., Burkard, R.E. & Pferschy, U. Inverse 1-center location problems with edge length augmentation on trees. Computing 86, 331–343 (2009). https://doi.org/10.1007/s00607-009-0070-7
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DOI: https://doi.org/10.1007/s00607-009-0070-7