The Rooted SCJ Median with Single Gene Duplications

Abstract

The median problem is a classical problem in genome rearrangements. It aims to compute a gene order that minimizes the sum of the genomic distances to k ≥ 3 given gene orders. This problem is intractable except in the related Single-Cut-or-Join and breakpoint rearrangement models. Here we consider the rooted median problem, where we assume one of the given genomes to be ancestral to the median, which is itself ancestral to the other genomes. We show that in the Single-Cutor-Join model with single gene duplications, the rooted median problem is NP-hard. We also describe an Integer Linear Program for solving this problem, which we apply to simulated data, showing high accuracy of the reconstructed medians.

Achieving large and distant ancestral genome inference by using an improved discrete quantum-behaved particle swarm optimization algorithm

“…Thus, Feijao et al developed an algorithmic approach for ancestral reconstruction of gene orders using the concept of intermediate genomes, which obtained a better reconstruction of the true ancestral genome [11]. Feijão et al later presented a closed equation for the single cut join (SCJ) distance model that accounts for duplications [12] and thereafter, introduced an integer linear program to solve the Median Problem but in a context where gene duplication events were now considered [13].…”