Performance Guarantees of Greedy Hierarchical Algorithm for Shortest Common Superstring Problem

Shortest Common Superstring is an NP-hard problem, which finds its application in DNA sequencing. As it often happens for problems from the NP-hard class, algorithms generating precise solutions can’t be used in practice due to their exponential complexity. Because of that approximation algorithms are widely used instead. Though their application puts some restrictions on the task (for instance, suboptimal solutions should be tolerated), they have proved to be quite effective and sometimes even precise. Unfortunately, though it has been almost 30 years since the first conjecture about the existence of a 2-optimal algorithm for the Shortest Common Superstring problem had been claimed, there is currently no polynomial algorithm which would be proven to satisfy this condition. Nevertheless, there are several algorithms whose efficiency hasn’t been studied yet, including the one this work concentrates on. Our study focuses on the recently published approximation algorithm for Shortest Common Superstring problem called Greedy Hierarchical Algorithm and aims to determine its approximation factor.