A Fast and Exact Algorithm for the Median of Three Problem--A Graph Decomposition Approach

Authors:
Andrew Wei Xu
Affiliations:
Department of Mathematics and Statistics, University of Ottawa, Canada K1N 6N5
Venue:
RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
Year:
2008

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Abstract

In a previous paper, we have shown that adequate subgraphs can be used to decompose multiple breakpoint graphs, achieving a dramatic speedup in solving the median problem. In this paper, focusing on the median of three problem, we prove more important properties about adequate subgraphs with rank 3 and discuss the algorithms inventorying simple adequate subgraphs. After finding simple adequate subgraphs of small sizes, we incorporate them into ASMedian, an algorithm to solve the median of three problem. Results on simulated data show dramatic speedup so that many instances can be solved very quickly, even ones containing hundreds or thousands of genes.