Duplicated Genes Reversal Distance under Gene Deletion Constraint by Integer Programming

Reversal distance between genomes can be used to estimate evolutionary distance between species. Recently, the problem of duplicated genes in reversal distance has been studied. Several proposed algorithms are based on heuristic approaches such as integer programming. However, in real genome comparison, the number of genes in each genome can be different due to gene insertion and deletion during the evolution. This observation was mentioned in El-mabrouk´s work. But this work did not consider the case of duplicated genes. In this paper, we study the reversal distance with duplicated genes as well as their deletion distance. The reversal lower bound is derived and compared with our proposed integer programming algorithm.