Parallel Architectures, Algorithms and Programming, International Symposium on (2011)

Tianjin, China

Dec. 9, 2011 to Dec. 11, 2011

ISBN: 978-0-7695-4575-2

pp: 47-51

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/PAAP.2011.15

ABSTRACT

The Min-Min problem of finding a disjoint-path pair with the length of the shorter path minimized is known to be NP-hard in general graphs. However, it remains an open problem whether the Min-Min problem is NP-hard in some special graph such as planar graphs. In this paper, for an st-outerplanar graph G = (V;E) which is a special planar graph that can be drawn in the plane with source vertex s and destination vertex t belong to the unbounded face of the drawing, we show that the vertex disjoint Min-Min problem is polynomial solvable therein by presenting an algorithm with a time complexity of O(jEj + jV j log jV j).

INDEX TERMS

Min-Min problem, planar graphs, NP-hard, polynomial-time algorithm, shortest path, disjoint path

CITATION

Hong Shen,
Longkun Guo,
"A Polynomial Algorithm for the Vertex Disjoint Min-Min Problem in Planar Graphs",

*Parallel Architectures, Algorithms and Programming, International Symposium on*, vol. 00, no. , pp. 47-51, 2011, doi:10.1109/PAAP.2011.15