Hardness of finding two edge-disjoint min-min paths in digraphs

Authors:
Longkun Guo;Hong Shen
Affiliations:
School of Computer Science, Univ. of Science and Technology of China;School of Computer Science, Univ. of Science and Technology of China and School of Computer Science, University of Adelaide, Australia
Venue:
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Year:
2011

Citing 6
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Abstract

The Min-Min problem of finding a disjoint path pair with the length of the shorter path minimized is known to be NP-complete and no K-approximation exists for any K ≥ 1 [1]. In this paper, we give a simpler proof of this result in general digraphs. We show that this proof can be extended to the problem in planar digraphs whose complexity was unknown previously. As a by-product, we show this problem remains NPcomplete even when all edge costs are equal (i.e. strongly NP-complete).