Greedy Shortest Common Superstring Approximation in Compact Space

TL;DR

This paper introduces a space-efficient implementation of the greedy heuristic for the shortest common superstring problem, enabling practical use on large datasets like DNA fragments.

Contribution

It provides the first time and space efficient implementation of the greedy heuristic for the shortest common superstring problem.

Findings

Works in O(n log σ) time and space

Uses roughly 5 n log σ bits of space on real datasets

Efficiently handles DNA fragment datasets

Abstract

Given a set of strings, the shortest common superstring problem is to find the shortest possible string that contains all the input strings. The problem is NP-hard, but a lot of work has gone into designing approximation algorithms for solving the problem. We present the first time and space efficient implementation of the classic greedy heuristic which merges strings in decreasing order of overlap length. Our implementation works in $O(n \log \sigma)$ time and bits of space, where $n$ is the total length of the input strings in characters, and $\sigma$ is the size of the alphabet. After index construction, a practical implementation of our algorithm uses roughly $5 n \log \sigma$ bits of space and reasonable time for a real dataset that consists of DNA fragments.