Greedy superstring conjecture

Determine whether the greedy superstring algorithm for the Shortest Common Superstring problem has approximation ratio at most 2, thereby establishing whether its worst-case approximation ratio is exactly 2.

Background

The Shortest Common Superstring problem asks for a shortest string containing every input string as a substring. The greedy algorithm repeatedly selects an ordered pair of strings with maximum overlap, merges them, and reinserts the merged string. Its simplicity and linear-time implementability contrast with the substantially more complicated best-known approximation algorithms.

The paper proves a lower bound of 2 for inputs whose strings have length at least 6, but does not establish the corresponding upper bound. Consequently, the conjecture that the greedy algorithm has approximation ratio exactly 2 remains unresolved; the best known general upper bound cited in the paper is 3.396.

References

At the same time, there~is~an~extremely simple greedy algorithm whose approximation ratio is~conjectured to~be equal to~$2$:

— The Greedy Superstring Algorithm Achieves Ratio 2 for Strings of Length 6 Already  (2608.20018 - Chukhin et al., 20 Aug 2026) in Section 1, "Greedy Superstring Conjecture"

However, despite its simplicity, its exact approximation ratio is unknown.

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