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A Tight Bound on Online Vertex Cover under Edge Arrivals

Zhihao Gavin Tang, Yuhao Zhang

For every deterministic fractional online vertex-cover algorithm and every ε>0, a finite bipartite edge-arrival instance forces a competitive ratio of at least 2−ε. The paper extends the lower bound to randomized integral or fractional algorithms against an oblivious adversary.

Sources for this record

What was already known

A factor-2 edge-arrival algorithm was known. Earlier lower bounds in other arrival models did not settle this edge-arrival problem.

AI involvement AI-centered

Tang and Zhang suggested the blueprint framework; GPT-5.6 Sol formulated the decisive reduction. The authors independently checked and explained it.

GPT-5.6 Sol supplied the decisive reduction after Tang and Zhang suggested the blueprint framework.

Importance Notable

Closes the gap between the known upper bound and the edge-arrival lower bound.

Limitations

The randomized claim is against an oblivious adversary. A previously cited 1.753 lower bound concerns general vertex arrivals, a different model.

Technical verification Formal (human)

Tang and Zhang expressly report independently checking the complete reduction and proof.

Independent checking

Independent author verification of the reduction and proof

Checker
Zhihao Gavin Tang and Yuhao Zhang, paper authors
Scope
The blueprint reduction and proof of the 2−ε edge-arrival lower bound
Basis
Reported by the linked checker
Evidence source

Human understanding Full

Tang and Zhang give and defend a detailed explanation of the reduction.

Correction and publication history