DCJ-indel Distance with Distinct Operation Costs

Abstract

The double-cut and join (DCJ) is a genomic operation that generalizes the typical mutations to which genomes are subject. The distance between two genomes, in terms of number of DCJ operations, can be computed in linear time. More powerful is the DCJ-indel model, which handles genomes with unequal contents, allowing, besides the DCJ operations, the insertion and/or deletion of pieces of DNA – named indel operations. It has been shown that the DCJ-indel distance can also be computed in linear time, assuming that the same cost is assigned to any DCJ or indel operation. In the present work we consider a new DCJ-indel distance in which the indel cost is distinct from and upper bounded by the DCJ cost. Considering that the DCJ cost is equal to 1, we set the indel cost equal to a positive constant w ≤ 1 and show that the distance can still be computed in linear time. This new distance generalizes the previous DCJ-indel distance considered in the literature (which uses the same cost for both types of operations).