Abstract
Computing the edit distance between two genomes under certain operations 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 easily computed for genomes without duplicate genes. In this paper, we study the edit distance for genomes with duplicate genes under a model that includes DCJ operations, insertions and deletions. We prove that computing the edit distance is equivalent to finding the optimal cycle decomposition of the corresponding adjacency graph, and give an approximation algorithm with an approximation ratio of 1.5 + ∈.
Highlights
The combinatorics and algorithmics of genomic rearrangements have been the subject of much research since the problem was formulated in the 1990s [1]
We reduce the problem of computing such an edit distance to finding the maximum number of certain cycles in the adjacency graph, we give a (1.5 + Î)-approximation algorithm
We show how to perform DCJ operations, insertions and deletions to transform S1 into S2 based on a decomposition of the corresponding adjacency graph
Summary
The combinatorics and algorithmics of genomic rearrangements have been the subject of much research since the problem was formulated in the 1990s [1]. We show how to perform DCJ operations, insertions and deletions to transform S1 into S2 based on a decomposition of the corresponding adjacency graph. Given two adjacency sets S1 and S2, and a decomposition D of the adjacency graph A = {S1 ∪ T2, S2 ∪ T1, E} with c helpful cycles and o odd-length paths, we can perform n - c - o/2 operations to transform S1 into S2, among which there are |T1| deletions, |T2| insertions and n - c - o/2 - |T1|-|T2| DCJ operations. □. In summary, based on Theorems 2 and 3, we have stated the equivalence of the problem of computing the edit distance and that of finding a valid decomposition with a maximum number of helpful cycles in an adjacency graph without telomeres.
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