Determine the best possible approximation ratio for shortest common superstring

Determine the best possible approximation ratio achievable for the shortest common superstring problem.

Background

The shortest common superstring problem is NP-hard and APX-hard, so research has focused on approximation algorithms. The paper notes that approximation guarantees have improved over several decades, but the optimal approximation threshold for the problem as a whole has not been established.

This question is distinct from the exact ratio of the greedy algorithm: it concerns the best possible approximation ratio achievable by any polynomial-time approximation approach for shortest common superstring.

References

Since Blum et al. gave the first constant-factor approximation algorithm, the best-known approximation ratio for SCS has been repeatedly improved for over 30 years, but the best possible ratio remains unknown.

— Disproving the Greedy Superstring Conjecture  (2609.01365 - Shibata, 1 Sep 2026) in Section 1, Introduction