Length-bounded disjoint paths in planar graphs ?
The following problem is considered: given: an undirected planar graph G=(V,E) embedded in , distinct pairs of vertices {r1,s1},,{rk,sk} of G adjacent to the unbounded face, positive integers b1,,bk and a function ; find: pairwise vertex-disjoint paths P1,,Pk such that for each i=1,,k, Pi is a ri?si-path and the sum of the l-length of all edges in Pi is at most bi. It is shown that the problem is NP-hard in the strong sense. A pseudo-polynomial-time algorithm is given for the case of k=2.
disjoint paths planar graphs complexity dynamic programming