Triangulating Vertex-Colored Graphs
SIAM Journal on Discrete Mathematics
Inferring Evolutionary History from DNA Sequences
SIAM Journal on Computing
Tree compatibility and inferring evolutionary history
Journal of Algorithms
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Two Strikes Against Perfect Phylogeny
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Incomplete Directed Perfect Phylogeny
SIAM Journal on Computing
Haplotyping with missing data via perfect path phylogenies
Discrete Applied Mathematics
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
On the Generalised Character Compatibility Problem for Non-branching Character Trees
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Journal of Computer and System Sciences
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In [3,2], the authors introduced the Generalised Cladistic Character Compatibility (GCCC) Problem which generalises a variant of the Perfect Phylogeny Problem in order to model better experiments in molecular biology showing that genes contain information for currently unexpressed traits, e.g., having teeth. In [3], the authors show that this problem is NP-complete and give some special cases which are polynomial. The authors also pose an open case of this problem where each character has only one generalised state, and each character tree is non-branching, a case that models these experiments particularly closely, which we call the Benham-Kannan-Warnow (BKW) Case. In [18], the authors study the complexity of a set of cases of the GCCC Problem for non-branching character trees when the phylogeny tree that is a solution to this compatibility problem is restricted to be either a tree, path or single-branch tree. In particular, they show that if the phylogeny tree must have only one branch, the BKW Case is polynomial-time solvable, by giving a novel algorithm based on PQ-trees used for the consecutive-ones property of binary matrices. In this work, we characterise the complexity of the remainder of the cases considered in [18] for the single-branch tree and the path. We show that some of the open cases are polynomial-time solvable, one by using an algorithm based on directed paths in the character trees similar to the algorithm in [2], and the second by showing that this case can be reduced to a polynomial-time solvable case of [18]. On the other hand, we will show that other open cases are NP-complete using an interesting variation of the ordering problems we study here. In particular, we show that the BKW Case for the path is NP-complete.