A Fast and Exact Algorithm for the Perfect Reversal Median Problem

Abstract

We study the problem of finding for the gene orders of three taxa a potential ancestral gene order such that the corresponding rearrangement scenario has a minimal number of reversals where each of the reversals has to preserve the common intervals of the given input gene orders. Common intervals identify sets of genes that occur consecutively in all input gene orders. The problem of finding such an ancestral gene order is called the perfect reversal median problem (pRMP). A tree based data structure for the representation of the common intervals of all input gene orders is used for the design and realization of a fast and exact algorithm--called TCIP--for solving the pRMP. It is known that for two given gene orders the minimum number of reversals to transfer one gene order into the other can be computed in polynomial time, whereas the corresponding problem with the restriction that common intervals should not be destroyed by the reversals is already NP-hard. Nevertheless, we show empirically on biological and artificial data that TCIP for the pRMP is usually even faster than the fastest exact algorithm (Caprara's median solver) for the reversal median problem (RMP), i.e., the corresponding problem in which the common intervals are not considered.