Triangulating Vertex-Colored Graphs
SIAM Journal on Discrete Mathematics
Inferring Evolutionary History from DNA Sequences
SIAM Journal on Computing
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Two Strikes Against Perfect Phylogeny
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Journal of Computer and System Sciences
ISBRA'11 Proceedings of the 7th international conference on Bioinformatics research and applications
Hi-index | 0.00 |
In [13], the authors introduced the Generalised Character Compatibility Problem as a generalisation of the Perfect Phylogeny Problem for a set of species. This generalised problem takes into account the fact that while a species may not be expressing a certain trait, i.e., having teeth, its DNA may contain data for this trait in a non-functional region. The authors showed that the Generalised Character Compatibility Problem is NP-complete for an instance of the problem involving five states, where the characters' state transition trees are branching. They also presented a class of instances of the problem that is polynomial-time solvable. The authors posed an open problem about the complexity of this problem when no branching is allowed in the character trees. They answered this question in [2], where they showed that for an instance in which each character tree is 0***1***2 (no branching), and only the states {1},{0,2},{0,1,2} are allowed, is NP-complete. This, however, does not provide an answer to the exact question posed in [3], which allows only one type of generalised state: {0,2}, called here the Benham-Kannan-Warnow (BKW) Case. In this paper, we study the complexity of various versions of this problem with non-branching character trees, depending on the set of states allowed, and depending on the restriction on the phylogeny tree: any tree, path or single-branch tree. In particular, we show that if the phylogeny tree is required to have only one branch: (a) the problem still remains NP-complete (for instance with states {1},{0,2},{0,1,2}), and (b) the problem is polynomial-time solvable in the BKW Case (with states {0},{1},{2},{0,2}). We show the second result by unveiling a surprising connection to the Consecutive-Ones Property (C1P) Problem, used for instance, in DNA physical mapping, interval graph recognition and data retrieval.