Heuristics for the inversion median problem.

Background: The study of genome rearrangements has become a mainstay of phylogenetics and comparative genomics. Fundamental in such a study is the median problem: given three genomes find a fourth that minimizes the sum of the evolutionary distances between itself and the given three. Many exact algorithms and heuristics have been developed for the inversion median problem, of which the best known is MGR.

Results: We present a unifying framework for median heuristics, which enables us to clarify existing strategies and to place them in a partial ordering. Analysis of this framework leads to a new insight: the best strategies continue to refer to the input data rather than reducing the problem to smaller instances. Using this insight, we develop a new heuristic for inversion medians that uses input data to the end of its computation and leverages our previous work with DCJ medians. Finally, we present the results of extensive experimentation showing that our new heuristic outperforms all others in accuracy and, especially, in running time: the heuristic typically returns solutions within 1% of optimal and runs in seconds to minutes even on genomes with 25'000 genes--in contrast, MGR can take days on instances of 200 genes and cannot be used beyond 1'000 genes.

Conclusion: Finding good rearrangement medians, in particular inversion medians, had long been regarded as the computational bottleneck in whole-genome studies. Our new heuristic for inversion medians, ASM, which dominates all others in our framework, puts that issue to rest by providing near-optimal solutions within seconds to minutes on even the largest genomes.