Fast approximation algorithms for fractional packing and covering problems
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Topological sorting of large networks
Communications of the ACM
CARTHAGENE: Constructing and Joining Maximum Likelihood Genetic Maps
Proceedings of the 5th International Conference on Intelligent Systems for Molecular Biology
Consensus Genetic Maps: A Graph Theoretic Approach
CSB '05 Proceedings of the 2005 IEEE Computational Systems Bioinformatics Conference
Consensus Genetic Maps as Median Orders from Inconsistent Sources
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Multilocus consensus genetic maps (MCGM): Formulation, algorithms, and results
Computational Biology and Chemistry
Efficient and accurate construction of genetic linkage maps from noisy and missing genotyping data
WABI'07 Proceedings of the 7th international conference on Algorithms in Bioinformatics
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We study the problem of merging genetic maps, when the individual genetic maps are given as directed acyclic graphs. The computational problem is to build a consensus map, which is a directed graph that includes and is consistent with all (or, the vast majority of) the markers in the input maps. However, when markers in the individual maps have ordering conflicts, the resulting consensus map will contain cycles. Here, we formulate the problem of resolving cycles in the context of a parsimonious paradigm that takes into account two types of errors that may be present in the input maps, namely, local reshuffles and global displacements. The resulting combinatorial optimization problem is, in turn, expressed as an integer linear program. A fast approximation algorithm is proposed, and an additional speedup heuristic is developed. Our algorithms were implemented in a software tool named MergeMap which is freely available for academic use. An extensive set of experiments shows that MergeMap consistently outperforms JoinMap, which is the most popular tool currently available for this task, both in terms of accuracy and running time. MergeMap is available for download at http://www.cs.ucr.edu/~yonghui/mgmap.html.