Constructing evolutionary trees in the presence of polymorphic characters
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Better methods for solving parsimony and compatibility
RECOMB '98 Proceedings of the second annual international conference on Computational molecular biology
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Tree compatibility and inferring evolutionary history
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Reconstructing the evolutionary history of natural languages
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Quasi-median graphs from sets of partitions
Discrete Applied Mathematics
From Quartets to Phylogenetic Trees
SOFSEM '98 Proceedings of the 25th Conference on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
On the Generalised Character Compatibility Problem for Non-branching Character Trees
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Upper and lower bounds for finding connected motifs in vertex-colored graphs
Journal of Computer and System Sciences
Exact algorithms for intervalizing colored graphs
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
ISBRA'11 Proceedings of the 7th international conference on Bioinformatics research and applications
Unique perfect phylogeny is NP-hard
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
An important connection between network motifs and parsimony models
RECOMB'06 Proceedings of the 10th annual international conference on Research in Computational Molecular Biology
On minimal vertex separators of dually chordal graphs: Properties and characterizations
Discrete Applied Mathematics
Sharp tractability borderlines for finding connected motifs in vertex-colored graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Unique perfect phylogeny is intractable
Theoretical Computer Science
| Hi-index | 0.01 |
This paper examines the class of vertex-colored graphs that can be triangulated without the introduction of edges between vertices of the same color. This is related to a fundamental and long-standing problem for numerical taxonomists, called the Perfect Phylogeny Problem. These problems are known to be polynomially equivalent and NP-complete. This paper presents a dynamic programming algorithm that can be used to determine whether a given vertex-colored graph can be so triangulated and that runs in $O((n+m(k-2))^{k+1})$ time, where the graph has $n$ vertices, $m$ edges, and $k$ colors. The corresponding algorithm for the Perfect Phylogeny Problem runs in $O(r^{k+1} k^{k+1} + sk^2 )$ time, where $s$ species are defined by $k$ $r$-state characters.