Improved Approximation Ratios for the Shortest Common Superstring Problem with Reverse Complements

TL;DR

This paper improves approximation ratios for the Shortest Common Superstring problem with Reverse Complements (SCS-RC), a bioinformatics problem, by extending existing algorithms and providing the first formal bounds for this variant.

Contribution

It extends MGREEDY and TGREEDY algorithms to SCS-RC, achieving better approximation ratios of 3.75 and 2.875, respectively, and provides the first formal guarantees for SCS-RC.

Findings

MGREEDY extension achieves 3.75-approximation

TGREEDY extension achieves 2.875-approximation

First formal approximation bounds for SCS-RC

Abstract

The Shortest Common Superstring (SCS) problem asks for the shortest string that contains each of a given set of strings as a substring. Its reverse-complement variant, the Shortest Common Superstring problem with Reverse Complements (SCS-RC), naturally arises in bioinformatics applications, where for each input string, either the string itself or its reverse complement must appear as a substring of the superstring. The well-known MGREEDY algorithm for the standard SCS constructs a superstring by first computing an optimal cycle cover on the overlap graph and then concatenating the strings corresponding to the cycles, while its refined variant, TGREEDY, further improves the approximation ratio. Although the original 4- and 3-approximation bounds of these algorithms have been successively improved for the standard SCS, no such progress has been made for the reverse-complement setting. A previous study extended MGREEDY to SCS-RC with a 4-approximation guarantee and briefly suggested that extending TGREEDY to the reverse-complement setting could achieve a 3-approximation. In this work, we strengthen these results by proving that the extensions of MGREEDY and TGREEDY to the reverse-complement setting achieve 3.75- and 2.875-approximation ratios, respectively. Our analysis extends the classical proofs for the standard SCS to handle the bidirectional overlaps introduced by reverse complements. These results provide the first formal improvement of approximation guarantees for SCS-RC, with the 2.875-approximate algorithm currently representing the best known bound for this problem.