Planar disjoint-paths completion

Authors:
Isolde Adler;Stavros G. Kolliopoulos;Dimitrios M. Thilikos
Affiliations:
Institut für Informatik, Goethe-Universität, Frankfurt am Main, Germany;Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece;Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece
Venue:
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Year:
2011

Citing 8
Cited 0

Regular Article: On the Complexity of DNA Physical Mapping

Advances in Applied Mathematics
Graph minors. XIII: the disjoint paths problem

Journal of Combinatorial Theory Series B
Tractability of Parameterized Completion Problems on Chordal, Strongly Chordal, and Proper Interval Graphs

SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Interval completion with few edges

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A shorter proof of the graph minor algorithm: the unique linkage theorem

Proceedings of the forty-second ACM symposium on Theory of computing
Finding topological subgraphs is fixed-parameter tractable

Proceedings of the forty-third annual ACM symposium on Theory of computing
Tight bounds for linkages in planar graphs

ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 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 explicit bound on the number of necessary additional edges if 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)·n2.