Breakthrough Tracker record

A preprint disproves the greedy superstring 2-approximation conjecture

Hiroki Shibata constructs instances for which the standard greedy shortest-common-superstring algorithm has approximation ratio approaching 9/4. This refutes the nearly four-decade conjecture that the ratio is at most 2.

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Stable ID
cs-greedy-superstring-conjecture-counterexample-2026
Revision
cs-greedy-superstring-conjecture-counterexample-2026.v1
Field
Computer Science · Algorithms, approximation and string combinatorics
Evidence
Tier 1 · Peer reviewed: No
Record state
Provisional · Provisional claimed counterexample
Last checked

AI role

The author reports that GPT-5.6 Sol, used through a custom harness, first discovered the counterexample and proof strategies. The author examined, simplified and verified the proof and takes responsibility for it.

Record details

Problem or result
The conjectured factor-2 guarantee for the greedy shortest-common-superstring algorithm
Authors
Hiroki Shibata
Institutions
Joint Graduate School of Mathematics for Innovation, Kyushu University
Result date
First-version preprint submitted September 1, 2026

Why it matters

Shortest common superstring is a foundational approximation problem with applications in sequence assembly and compression. The construction raises the greedy algorithm’s known worst-case lower bound from 2 to 9/4.

Limits

The result is a first-version preprint with no located peer review or independent verification. It establishes a lower bound approaching 9/4; it does not determine the exact worst-case ratio, whose known upper bound remains 3.

Sources

  1. Primary: Shibata, greedy-superstring counterexample

Correction and revision history

  1. 2026-09-04 — Added after primary-source, scope, status, AI-role and limitation review.

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