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)·n 2.
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Adler, I., Kolliopoulos, S.G., Thilikos, D.M. (2012). Planar Disjoint-Paths Completion. In: Marx, D., Rossmanith, P. (eds) Parameterized and Exact Computation. IPEC 2011. Lecture Notes in Computer Science, vol 7112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28050-4_7
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DOI: https://doi.org/10.1007/978-3-642-28050-4_7
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