On the complexity of the edge-disjoint min-min problem in planar digraphs

Authors:
Longkun Guo;Hong Shen
Affiliations:
School of Computer Science and Mathematics, Fuzhou University, China;School of Computer and Information Technology, Beijing Jiaotong University, China and School of Computer Science, University of Adelaide, Australia
Venue:
Theoretical Computer Science
Year:
2012

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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 (Xu et al., 2006) [1]. In this paper, we prove that in planar digraphs the edge-disjoint min-min problem remains NP-complete and admits no K-approximation for any K1 unless P=NP. As a by-product, we show that this problem remains NP-complete even when all edge costs are equal (i.e., stronglyNP-complete). To our knowledge, this is the first NP-completeness proof for the edge-disjoint min-min problem in planar digraphs.