On finding the strongly connected components in a directed graph
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
INFORMS Journal on Computing
Consensus Genetic Maps: A Graph Theoretic Approach
CSB '05 Proceedings of the 2005 IEEE Computational Systems Bioinformatics Conference
Reversal distance for partially ordered genomes
Bioinformatics
Removing Noise and Ambiguities from Comparative Maps in Rearrangement Analysis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Consensus Genetic Maps as Median Orders from Inconsistent Sources
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Following various genetic mapping techniques conducted on different segregating populations, one or more genetic maps are obtained for a given species. However, recombination analyses and other methods for gene mapping often fail to resolve the ordering of some pairs of neighboring markers, thereby leading to sets of markers ambiguously mapped to the same position. Each individual map is thus a partial order defined on the set of markers, and can be represented as a Directed Acyclic Graph (DAG). In this paper, given a phylogenetic tree with a set of DAGs labeling each leaf (species), the goal is to infer, at each leaf, a single combined DAG that is as resolved as possible, considering the complementary information provided by individual maps, and the phylogenetic information provided by the species tree. After combining the individual maps of a leaf into a single DAG, we order incomparable markers by using two successive heuristics for minimizing two distances on the species tree: the breakpoint distance, and the Kemeny distance. We apply our algorithms to the plant species represented in the Gramene database, and we evaluate the simplified maps we obtained.