The inverse 1-maxian problem with edge length modification

Elisabeth Gassner ()
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Elisabeth Gassner: Graz University of Technology

Journal of Combinatorial Optimization, 2008, vol. 16, issue 1, No 5, 50-67

Abstract: Abstract We consider the problem of modifying the lengths of the edges of a graph at minimum cost such that a prespecified vertex becomes a 1-maxian with respect to the new edge lengths. The inverse 1-maxian problem with edge length modification is shown to be strongly $\mathcal{N}\mathcal{P}$ -hard and remains weakly $\mathcal{NP}$ -hard even on series-parallel graphs. Moreover, a transformation of the inverse 1-maxian problem with edge length modification on a tree to a minimum cost circulation problem is given which solves the original problem in $\mathcal{O}(n\log n)$ .

Keywords: Obnoxious location; Maxian; Inverse problem; Complexity; Tree (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (14)

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DOI: 10.1007/s10878-007-9098-9

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