Computing the breakpoint distance between partially ordered genomes

The total order of genes or markers on a chromosome is crucial for most comparative genomics studies. However, current gene mapping efforts might only suffice to provide a partial order of the genes on a chromosome. Several different genes or markers might be mapped at the same position due to the low resolution of gene mapping or missing data. Moreover, conflicting datasets might give rise to the ambiguity of gene order. In this paper, we consider the reversal distance and breakpoint distance problems for partially ordered genomes. We first prove that these problems are nondeterministic polynomial-time (NP)-hard, and then give an efficient heuristic algorithm to compute the breakpoint distance between partially ordered genomes. The algorithm is based on an efficient approximation algorithm for a natural generalization of the well-known feedback vertex set problem, and has been tested on both simulated and real biological datasets. The experimental results demonstrate that our algorithm is quite effective for estimating the breakpoint distance between partially ordered genomes and for inferring the gene (total) order.