Automata, Languages and Programming
Volume 4051 of the series Lecture Notes in Computer Science pp 667-678
Fixed Parameter Tractability of Binary Near-Perfect Phylogenetic Tree Reconstruction
- Guy E. BlellochAffiliated withComputer Science Department, CMU
- , Kedar DhamdhereAffiliated withGoogle Inc
- , Eran HalperinAffiliated withICSI
- , R. RaviAffiliated withTepper School of Business, CMU
- , Russell SchwartzAffiliated withDept Biological Sciences, CMU
- , Srinath SridharAffiliated withComputer Science Department, CMU
Abstract
We consider the problem of finding a Steiner minimum tree in a hypercube. Specifically, given n terminal vertices in an m dimensional cube and a parameter q, we compute the Steiner minimum tree in time O(72 q + 8 q nm 2), under the assumption that the length of the minimum Steiner tree is at most m + q.
This problem has extensive applications in taxonomy and biology. The Steiner tree problem in hypercubes is equivalent to the phylogeny (evolutionary tree) reconstruction problem under the maximum parsimony criterion, when each taxon is defined over binary states. The taxa, character set and mutation of a phylogeny correspond to terminal vertices, dimensions and traversal of a dimension in a Steiner tree. Phylogenetic trees that mutate each character exactly once are called perfect phylogenies and their size is bounded by the number of characters. When a perfect phylogeny consistent with the data set exists it can be constructed in linear time. However, real data sets often do not admit perfect phylogenies. In this paper, we consider the problem of reconstructing near-perfect phylogenetic trees (referred to as BNPP). A near-perfect phylogeny relaxes the perfect phylogeny assumption by allowing at most q additional mutations. We show for the first time that the BNPP problem is fixed parameter tractable (FPT) and significantly improve the previous asymptotic bounds.
- Title
- Fixed Parameter Tractability of Binary Near-Perfect Phylogenetic Tree Reconstruction
- Book Title
- Automata, Languages and Programming
- Book Subtitle
- 33rd International Colloquium, ICALP 2006, Venice, Italy, July 10-14, 2006, Proceedings, Part I
- Pages
- pp 667-678
- Copyright
- 2006
- DOI
- 10.1007/11786986_58
- Print ISBN
- 978-3-540-35904-3
- Online ISBN
- 978-3-540-35905-0
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- 4051
- Series ISSN
- 0302-9743
- Publisher
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Topics
- Industry Sectors
- eBook Packages
- Editors
-
- Michele Bugliesi (16)
- Bart Preneel (17)
- Vladimiro Sassone (18)
- Ingo Wegener (19)
- Editor Affiliations
-
- 16. Dipartimento di Informatica, Università Ca’ Foscari
- 17. Interdisciplinary Institute for BroadBand Technology (IBBT)
- 18. ECS, University of Southampton
- 19. FB Informatik, Univ. Dortmund
- Authors
-
- Guy E. Blelloch (20)
- Kedar Dhamdhere (21)
- Eran Halperin (22)
- R. Ravi (23)
- Russell Schwartz (24)
- Srinath Sridhar (20)
- Author Affiliations
-
- 20. Computer Science Department, CMU,
- 21. Google Inc, Mountain View, CA
- 22. ICSI, 1947 Center St, Berkeley, CA
- 23. Tepper School of Business, CMU,
- 24. Dept Biological Sciences, CMU,
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