On improving the approximation ratio of the r-shortest common superstring problem

TL;DR

This paper advances approximation algorithms for the r-shortest common superstring problem, improving the ratio for specific string lengths and moving closer to the theoretical lower bound.

Contribution

It extends previous approaches to achieve better approximation ratios for r-SCS, especially for r up to 7, surpassing prior bounds for these cases.

Findings

Improved approximation ratio for r<=7

Ratio less than or equal to 2 for r<=6

Extension of Golonev et al.'s approach

Abstract

The Shortest Common Superstring problem (SCS) consists, for a set of strings S = {s_1,...,s_n}, in finding a minimum length string that contains all s_i, 1<= i <= n, as substrings. While a 2+11/30 approximation ratio algorithm has recently been published, the general objective is now to break the conceptual lower bound barrier of 2. This paper is a step ahead in this direction. Here we focus on a particular instance of the SCS problem, meaning the r-SCS problem, which requires all input strings to be of the same length, r. Golonev et al. proved an approximation ratio which is better than the general one for r<= 6. Here we extend their approach and improve their approximation ratio, which is now better than the general one for r<= 7, and less than or equal to 2 up to r = 6.