Greedy-reduction from Shortest Linear Superstring to Shortest Circular Superstring

TL;DR

This paper explores the Shortest Circular Superstring problem, establishing its NP-completeness and proposing a new conjecture on its approximation ratio, thus advancing understanding of circular string superstring problems.

Contribution

It demonstrates the NP-completeness of the Shortest Circular Superstring problem and introduces a novel conjecture on its approximation ratio.

Findings

Proves NP-completeness of the problem

Establishes a link between linear and circular superstring problems

Proposes a new conjecture on approximation ratios

Abstract

A superstring of a set of strings correspond to a string which contains all the other strings as substrings. The problem of finding the Shortest Linear Superstring is a well-know and well-studied problem in stringology. We present here a variant of this problem, the Shortest Circular Superstring problem where the sought superstring is a circular string. We show a strong link between these two problems and prove that the Shortest Circular Superstring problem is NP-complete. Moreover, we propose a new conjecture on the approximation ratio of the Shortest Circular Superstring problem.