Divide-and-conquer approach for the exemplar breakpoint distance

A one-to-one correspondence between the sets of genes in the two genomes being compared is necessary for the notions of breakpoint and reversal distances. To compare genomes where there are paralogous genes, Sankoff formulated the exemplar distance problem as a general version of the genome rearrangement problem. Unfortunately, the problem is NP-hard even for the breakpoint distance.

This paper proposes a divide-and-conquer approach for calculating the exemplar breakpoint distance between two genomes with multiple gene families. The combination of our approach and Sankoff's branch-and-bound technique leads to a practical program to answer this question. Tests with both simulated and real datasets show that our program is much more efficient than the existing program that is based only on the branch-and-bound technique.

Code for the program is available from the authors.