Planar Disjoint-Paths Completion

Isolde Adler, Stavros G. Kolliopoulos, Dimitrios M. Thilikos
2015 Algorithmica  
We introduce Planar Disjoint Paths Completion, a completion counterpart of the Disjoint Paths problem, and study its parameterized complexity. The problem can be stated as follows: given a, not necessarily connected, plane graph G, k pairs of terminals, and a face F of G, find a minimum-size set of edges, if one exists, to be added inside F so that the embedding remains planar and the pairs become connected by k disjoint paths in the augmented network. Our results are twofold: first, we give an
more » ... upper bound on the number of necessary additional edges when a solution exists. This bound is a function of k, independent of the size of G. Second, we show that the problem is fixed-parameter tractable, in particular, it can be solved in time f (k) · n 2 .
doi:10.1007/s00453-015-0046-2 fatcat:ufznjk6n4baqfm5oxvyyuie2we