On the Greedy Algorithm for the Shortest Common Superstring Problem with Reversals

TL;DR

This paper introduces an improved greedy algorithm for the Shortest Common Superstring with Reversals problem, achieving a 50% approximation ratio and providing a linear-time implementation, advancing solutions for string superstring problems.

Contribution

It presents a natural adaptation of the classical greedy algorithm for SCS with reversals, achieving an optimal compression ratio of 1/2 and offering a linear-time implementation.

Findings

Achieves a 1/2 approximation ratio for SCS with reversals

Provides a linear-time implementation of the algorithm

Improves upon the previous 4-approximation algorithm

Abstract

We study a variation of the classical Shortest Common Superstring (SCS) problem in which a shortest superstring of a finite set of strings $S$ is sought containing as a factor every string of $S$ or its reversal. We call this problem Shortest Common Superstring with Reversals (SCS-R). This problem has been introduced by Jiang et al., who designed a greedy-like algorithm with length approximation ratio $4$. In this paper, we show that a natural adaptation of the classical greedy algorithm for SCS has (optimal) compression ratio $\frac12$, i.e., the sum of the overlaps in the output string is at least half the sum of the overlaps in an optimal solution. We also provide a linear-time implementation of our algorithm.