LATIN 2012: Theoretical Informatics
Volume 7256 of the series Lecture Notes in Computer Science pp 195-206
Solving the 2-Disjoint Connected Subgraphs Problem Faster Than 2 n
- Marek CyganAffiliated withInstitute of Informatics, University of Warsaw
- , Marcin PilipczukAffiliated withInstitute of Informatics, University of Warsaw
- , Michał PilipczukAffiliated withDepartment of Informatics, University of Bergen
- , Jakub Onufry WojtaszczykAffiliated withGoogle Inc.
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.
- Title
- Solving the 2-Disjoint Connected Subgraphs Problem Faster Than 2 n
- Book Title
- LATIN 2012: Theoretical Informatics
- Book Subtitle
- 10th Latin American Symposium, Arequipa, Peru, April 16-20, 2012. Proceedings
- Pages
- pp 195-206
- Copyright
- 2012
- DOI
- 10.1007/978-3-642-29344-3_17
- Print ISBN
- 978-3-642-29343-6
- Online ISBN
- 978-3-642-29344-3
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- 7256
- Series ISSN
- 0302-9743
- Publisher
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Topics
- Industry Sectors
- eBook Packages
- Editors
-
- David Fernández-Baca (16)
- Editor Affiliations
-
- 16. Department of Computer Science, Iowa State University
- Authors
-
- Marek Cygan (17)
- Marcin Pilipczuk (17)
- Michał Pilipczuk (18)
- Jakub Onufry Wojtaszczyk (19)
- Author Affiliations
-
- 17. Institute of Informatics, University of Warsaw, Poland
- 18. Department of Informatics, University of Bergen, Norway
- 19. Google Inc., Warsaw, Poland
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