Sorting by Reversals: A Faster Approach for Building Overlap Forest

Abstract

The problem of computing the reversal distance and determining a sequence of reversals to transform a genome in molecular biology is a powerful tool to derive relationships between genes. Given two signed permutations, we need to find the shortest sequence of reversals to transform one into another. The foremost polynomial-time algorithm to calculate the reversal distance used an overlap graph formed from the permutation to find connected components and then identified graph structures like hurdles. Previous researchers have used a Union-Find structure, an $\mathbf{O}(\mathbf{n}\alpha(\mathbf{n}))$ algorithm ($\alpha$->inverse Ackerman function) to determine the connected components. A linear time algorithm for finding the connected components, which was a faster implementation of the existing works was proposed later. This algorithm is applied to an unsigned extension of the signed permutation. In the first scan, cycles in a breakpoint graph were located. Then in a second scan, an overlap forest is formed which gave all the connected components of the permutation. In this paper, we optimize the existing algorithm to construct the overlap forest by reducing a scan of the unsigned permutation.