Consensus Genetic Maps as Median Orders from Inconsistent Sources

A genetic map is an ordering of genetic markers calculated from a population of known lineage. Although, traditionally, a map has been generated from a single population for each species, recently, researchers have created maps from multiple populations. In the face of these new data, we address the need to find a consensus map--a map that combines the information from multiple partial and possibly inconsistent input maps. We model each input map as a partial order and formulate the consensus problem as finding a median partial order. Finding the median of multiple total orders (preferences or rankings) is a well-studied problem in social choice. We choose to find the median by using the weighted symmetric difference distance, which is a more general version of both the symmetric difference distance and the Kemeny distance. Finding a median order using this distance is NP-hard. We show that, for our chosen weight assignment, a median order satisfies the positive responsiveness, extende...

• Type: Journal
• Year: 2008
• Where: TCBB
• Authors: Benjamin G. Jackson, Patrick S. Schnable, Srinivas Aluru
• Keywords: Median Order, Median Partial Order, Symmetric Difference Distance, TCBB 2008