A fast and effective heuristic for the feedback arc set problem
Information Processing Letters
A tight analysis of the greedy algorithm for set cover
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
Communications of the ACM
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
Discrete Optimization Algorithms with Pascal Programs
Discrete Optimization Algorithms with Pascal Programs
CARTHAGENE: Constructing and Joining Maximum Likelihood Genetic Maps
Proceedings of the 5th International Conference on Intelligent Systems for Molecular Biology
Transforming men into mice (polynomial algorithm for genomic distance problem)
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Introduction to Algorithms and Java CD-ROM
Introduction to Algorithms and Java CD-ROM
Trade-offs for fully dynamic transitive closure on DAGs: breaking through the O(n2 barrier
Journal of the ACM (JACM)
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Consensus Genetic Maps: A Graph Theoretic Approach
CSB '05 Proceedings of the 2005 IEEE Computational Systems Bioinformatics Conference
A computational study of the Kemeny rule for preference aggregation
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
RCG'05 Proceedings of the 2005 international conference on Comparative Genomics
Fast and high precision algorithms for optimization in large-scale genomic problems
Computational Biology and Chemistry
A Phylogenetic Approach to Genetic Map Refinement
RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
Accurate Construction of Consensus Genetic Maps via Integer Linear Programming
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Studies in computational aspects of voting: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
Parameterized enumeration of (locally-) optimal aggregations
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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A genetic map is an ordering of geneticmarkers calculated from a population of known lineage.While traditionally a map has been generated from a singlepopulation for each species, recently researchers have createdmaps from multiple populations. In the face of thesenew data, we address the need to find a consensus map — a map that combines the information from multiple partialand possibly inconsistent input maps. We model eachinput map as a partial order and formulate the consensusproblem as finding a median partial order. Finding themedian of multiple total orders (preferences or rankings)is a well studied problem in social choice. We choose tofind the median using the weighted symmetric differencedistance, a more general version of both the symmetricdifference distance and the Kemeny distance. Finding amedian order using this distance is NP-hard. We showthat for our chosen weight assignment, a median ordersatisfies the positive responsiveness, extended Condorcet,and unanimity criteria. Our solution involves finding themaximum acyclic subgraph of a weighted directed graph.We present a method that dynamically switches betweenan exact branch and bound algorithm and a heuristicalgorithm, and show that for real data from closely relatedorganisms, an exact median can often be found.We presentexperimental results using seven populations of the cropplant Zea mays.