An Exact Algorithm to Compute the Double-Cut-and-Join Distance for Genomes with Duplicate Genes

Abstract

Computing the edit distance between two genomes is a basic problem in the study of genome evolution. The double-cut-and-join (DCJ) model has formed the basis for most algorithmic research on rearrangements over the last few years. The edit distance under the DCJ model can be computed in linear time for genomes without duplicate genes, while the problem becomes NP-hard in the presence of duplicate genes. In this article, we propose an integer linear programming (ILP) formulation to compute the DCJ distance between two genomes with duplicate genes. We also provide an efficient preprocessing approach to simplify the ILP formulation while preserving optimality. Comparison on simulated genomes demonstrates that our method outperforms MSOAR in computing the edit distance, especially when the genomes contain long duplicated segments. We also apply our method to assign orthologous gene pairs among human, mouse, and rat genomes, where once again our method outperforms MSOAR.

Approximating the DCJ distance of balanced genomes in linear time

“…We compare our algorithm with Shao et al’s ILP [4] (GREDU software package) on simulated datasets. Given two genomes, the ILP based experiments first build the adjacency graph, followed by capping of the telomeres, fixing some safe cycles of length two, and finally invoking an ILP solver to obtain an optimal solution with a time limit of 2 h. The experiments for both approaches were performed on an Intel i7 3.4GHz (4 cores) machine.…”

“…Following [4], we simulate artificial genomes with segmental duplications and DCJs. We uniformly select a position to start duplicating a segment of the genome and place the new copy to a new position.…”

“…This so called DCJ distance with duplicates for balanced genomes problem is NP-hard [4]. Our algorithm works on input genomes where the amount of duplicates is bounded by k , the maximum number of duplicates of any gene in the input genomes.…”

“…For genomes without duplicate genes, there are linear time algorithms to compute the distance allowing only DCJ operations [2]. On the other hand, for genomes with duplicate genes, computing the rearrangement distance is NP-hard, even when the genomes have exactly the same number of occurrences of each gene in each genome ( balanced genomes ) and only DCJ operations are allowed [3, 4]. …”

“…When genomes have duplicate genes, problem DCJ- distance becomes NP-hard [4]. In the same paper, the authors present an exact, exponential-time algorithm for its solution, phrased in form of an Integer Linear Program (ILP).…”