Sciweavers

Share
ISAAC
2009
Springer

On Shortest Disjoint Paths in Planar Graphs

9 years 10 months ago
On Shortest Disjoint Paths in Planar Graphs
For a graph G and a collection of vertex pairs {(s1, t1), . . . , (sk, tk)}, the k disjoint paths problem is to find k vertex-disjoint paths P1, . . . , Pk, where Pi is a path from si to ti for each i = 1, . . . , k. In the corresponding optimization problem, the shortest disjoint paths problem, the vertex-disjoint paths Pi have to be chosen such that a given objective function is minimized. We consider two different objectives, namely minimizing the total path length (minimum sum, or short: min-sum), and minimizing the length of the longest path (min-max), for k = 2, 3. min-sum: We extend recent results by Colin de Verdi`ere and Schrijver to prove that, for a planar graph and for terminals adjacent to at most two faces, the Min-Sum 2 Disjoint Paths Problem can be solved in polynomial time. We also prove that, for six terminals adjacent to one face in any order, the Min-Sum 3 Disjoint Paths Problem can be solved in polynomial time. min-max: The Min-Max 2 Disjoint Paths Problem is kn...
Yusuke Kobayashi, Christian Sommer 0002
Added 25 Jul 2010
Updated 25 Jul 2010
Type Conference
Year 2009
Where ISAAC
Authors Yusuke Kobayashi, Christian Sommer 0002
Comments (0)
books