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Algorithmica

, Volume 76, Issue 2, pp 401–425 | Cite as

Planar Disjoint-Paths Completion

  • Isolde Adler
  • Stavros G. Kolliopoulos
  • Dimitrios M. ThilikosEmail author
Article
  • 205 Downloads

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, not necessarily connected, plane graph Gk 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 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 \(f(k)\cdot n^{2}\).

Keywords

Completion problems Disjoint paths Planar graphs 

Notes

Acknowledgments

We wish to thank the anonymous reviewers of an earlier version of this paper for valuable comments and suggestions.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Isolde Adler
    • 1
  • Stavros G. Kolliopoulos
    • 2
  • Dimitrios M. Thilikos
    • 3
    • 4
    Email author
  1. 1.Institut für InformatikGoethe-UniversitätFrankfurtGermany
  2. 2.Department of Informatics and TelecommunicationsNational and Kapodistrian University of AthensAthensGreece
  3. 3.Department of MathematicsUniversity of AthensAthensGreece
  4. 4.AlGCo Project TeamCNRS, LIRMMMontpellierFrance

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