On the complexity of the edge-disjoint min-min problem in undirected graphs
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2011
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Guo, L.
Shen, H.
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Conference paper
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Proceedings of the 3rd International Conference on Computer Research and Development, 11-13 March, 2011, Shanghai: pp.150-154
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Longkun Guo and Hong Shen
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International Conference on Computer Research and Development (3rd : 2011 : Shanghai)
Abstract
The min-min problem of finding a disjointpath pair with the length of the shorter path minimized is known to be NP-complete and admits no K-approximation for any K > 1 in the general case [1]. In this paper, we show that Bhatia et al [2]’s NP-complete proof, a claim of correction to Xu et al’s proof [1], for the edge-disjoint minmin problem in undirected graphs is incorrect by giving a counter example that is an unsatisfiable 3SAT instance but classified as a satisfiable 3SAT instance in Bhatia et al’s proof [2]. We then give a correct proof of NP-completeness of this problem in undirected graphs.
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© Copyright 2011 IEEE