Solving the 2-Disjoint Connected Subgraphs Problem Faster Than 2n

  • Marek Cygan
  • Marcin Pilipczuk
  • Michał Pilipczuk
  • Jakub Onufry Wojtaszczyk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7256)

Abstract

The 2-Disjoint Connected Subgraphs problem, given a graph along with two disjoint sets of terminals Z 1 ,Z 2 , asks whether it is possible to find disjoint sets A 1 ,A 2 , such that Z 1 ⊆ A 1 , Z 2 ⊆ A 2 and A 1 ,A 2 induce connected subgraphs. While the naive algorithm runs in O(2 n n O(1)) time, solutions with complexity of form O((2 − ε) n ) have been found only for special graph classes [15, 19]. In this paper we present an O(1.933 n ) algorithm for 2-Disjoint Connected Subgraphs in general case, thus breaking the 2 n barrier. As a counterpoise of this result we show that if we parameterize the problem by the number of non-terminal vertices, it is hard both to speed up the brute-force approach and to find a polynomial kernel.

Keywords

Polynomial Kernel Reduction Rule Valid Solution Articulation Point Subgraph Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marek Cygan
    • 1
  • Marcin Pilipczuk
    • 1
  • Michał Pilipczuk
    • 2
  • Jakub Onufry Wojtaszczyk
    • 3
  1. 1.Institute of InformaticsUniversity of WarsawPoland
  2. 2.Department of InformaticsUniversity of BergenNorway
  3. 3.Google Inc.WarsawPoland

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