Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Reconstructing a history of recombinations from a set of sequences
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
Reconstructing reticulate evolution in species: theory and practice
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Phylogenetic Networks: Modeling, Reconstructibility, and Accuracy
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
The Number of Recombination Events in a Sample History: Conflict Graph and Lower Bounds
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
The Fine Structure of Galls in Phylogenetic Networks
INFORMS Journal on Computing
Reconstructing Recombination Network from Sequence Data: The Small Parsimony Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Computing the Hybridization Number of Two Phylogenetic Trees Is Fixed-Parameter Tractable
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Algorithms for Efficient Near-Perfect Phylogenetic Tree Reconstruction in Theory and Practice
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
ReCombinatorics: Combinatorial Algorithms for Studying the History of Recombination in Populations
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Mixed Integer Linear Programming for Maximum-Parsimony Phylogeny Inference
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Drawing Rooted Phylogenetic Networks
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Counting Faces in Split Networks
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
The Structure of Level-k Phylogenetic Networks
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Parsimony Score of Phylogenetic Networks: Hardness Results and a Linear-Time Heuristic
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Comparative Genomics and Extensive Recombinations in Phage Communities
RECOMB-CG '09 Proceedings of the International Workshop on Comparative Genomics
Beyond galled trees: decomposition and computation of galled networks
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
Efficiently finding the most parsimonious phylogenetic tree via linear programming
ISBRA'07 Proceedings of the 3rd international conference on Bioinformatics research and applications
ISBRA'07 Proceedings of the 3rd international conference on Bioinformatics research and applications
Bubbles: alternative splicing events of arbitrary dimension in splicing graphs
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Phylogenetic network inferences through efficient haplotyping
WABI'06 Proceedings of the 6th international conference on Algorithms in Bioinformatics
Optimizing Phylogenetic Networks for Circular Split Systems
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Fast algorithms for computing the tripartition-based distance between phylogenetic networks
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Fixed parameter tractability of binary near-perfect phylogenetic tree reconstruction
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Reconstructing an ultrametric galled phylogenetic network from a distance matrix
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Reconstruction of reticulate networks from gene trees
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Efficient and practical algorithms for deducing the history of recombination in populations
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Simple reconstruction of binary near-perfect phylogenetic trees
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Blocks and Cut Vertices of the Buneman Graph
SIAM Journal on Discrete Mathematics
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Phylogenetic networks are models of evolution that go beyond trees, allowing biological operations that are not consistent with tree-like evolution. One of the most important of these biological operations is recombination between two sequences (homologous chromosomes). The algorithmic problem of reconstructing a history of recombinations, or determining the minimum number of recombinations needed, has been studied in a number of papers [10, 11, 12, 23, 24, 25, 16, 13, 14, 6, 9, 8, 18, 19, 15, 1]. In [9, 6, 10, 8, 1] we introduced and used “conflict graphs” and “incompatibility graphs” to compute lower bounds on the minimum number of recombinations needed, and to efficiently solve constrained cases of the minimization problem. In those results, the non-trivial connected components of the graphs were the key features that were used. In this paper we more fully develop the structural importance of non-trivial connected components of the incompatibility graph, to establish a fundamental decomposition theorem about phylogenetic networks. The result applies to phylogenetic networks where cycles reflect biological phenomena other than recombination, such as recurrent mutation and lateral gene transfer. The proof leads to an efficient O(nm2) time algorithm to find the underlying maximal tree structure defined by the decomposition, for any set of n sequences of length m each. An implementation of that algorithm is available. We also report on progress towards resolving the major open problem in this area.