Characterizations and algorithmic applications of chordal graph embeddings
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Listing all potential maximal cliques of a graph
Theoretical Computer Science
Two Strikes Against Perfect Phylogeny
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Space-optimal, backtracking algorithms to list the minimal vertex separators of a graph
Discrete Applied Mathematics
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Reducing problems in unrooted tree compatibility to restricted triangulations of intersection graphs
WABI'12 Proceedings of the 12th international conference on Algorithms in Bioinformatics
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The multistate perfect phylogeny problem is a classic problem in computational biology. When no perfect phylogeny exists, it is of interest to find a set of characters to remove in order to obtain a perfect phylogeny in the remaining data. This is known as the character removal problem. We show how to use chordal graphs and triangulations to solve the character removal problem for an arbitrary number of states, which was previously unsolved. We outline a preprocessing technique that speeds up the computation of the minimal separators of a graph. Minimal separators are used in our solution to the missing data character removal problem and to Gusfield's solution of the perfect phylogeny problem with missing data.