What was already known
Greedy’s one-half guarantee was known, but improving it with one pass and semi-streaming memory had been open for more than two decades. The authors’ earlier blueprint framework gave a weaker lower bound.
AI involvement
Assadi, Jiang and Xiang built the framework and optimal relaxation. They credit Claude Fable and GPT-5.6 Sol with the random-walk construction idea; the authors completed the blueprint, checked its constraints and computed its value.
The model-origin random-walk step is explicitly called the crux of the final blueprints, but the framework, relaxation and completed proof involved substantial human mathematical work.
Importance
The random-walk blueprints close the approximation gap in this streaming model.
Limitations
The reported author check covers blueprint constraints and value, not a completed check of the full lower-bound deduction. Online preemption and vertex-cover corollaries are distinct consequences.
Technical verification
Xiang reports that the team verified the final blueprint constraints and approximation calculation. That is a direct check of the central construction, but no complete check of the second paper's full lower-bound deduction is documented; Xiang states this paper had not yet received peer review. The Lean proof he mentions belongs to the first framework paper, not this construction.
Independent checking
Constructing the final blueprint, verifying constraints and calculating its value
- Checker
- Sepehr Assadi, Max Jiang and Mars Xiang, as reported by Xiang
- Scope
- The final random-walk blueprint's constraints and approximation ratio
- Basis
- Reported by the linked checker
Human understanding
Xiang gives a human explanation of the blueprint framework, the relaxation, the random-walk idea's origin and how the final construction produces the one-half bound.
Correction and publication history
The random-walk blueprints close the approximation gap in this streaming model.
Read this published revision