Three partition refinement algorithms
SIAM Journal on Computing
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Algorithms on strings, trees, and sequences: computer science and computational biology
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Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Efficient Reconstruction of Phylogenetic Networks with Constrained Recombination
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
A certifying algorithm for the consecutive-ones property
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
File searching using variable length keys
IRE-AIEE-ACM '59 (Western) Papers presented at the the March 3-5, 1959, western joint computer conference
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Construction of aho corasick automaton in linear time for integer alphabets
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
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A graph model for a set S of splits of a set X consists of a graph and a map from X to the vertices of the graph such that the inclusion-minimal cuts of the graph represent S. Phylogenetic trees are graph models in which the graph is a tree. We show that the model can be generalized to a cactus (i.e. a tree of edges and cycles) without losing computational efficiency. A cactus can represent a quadratic rather than linear number of splits in linear space. We show how to decide in linear time in the size of a succinct representation of S whether a set of splits has a cactus model, and if so construct it within the same time bounds. As a byproduct, we show how to construct the subset of all compatible splits and a maximal compatible set of splits in linear time. Note that it is NP-complete to find a compatible subset of maximum size. Finally, we briefly discuss further generalizations of tree models.