Tight Bound for Online Vertex Cover under Edge Arrivals
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Statement
What is the optimal competitive ratio for online vertex cover when edges arrive one at a time? The paper proves a tight factor-2 lower bound via a reduction in the blueprint framework of Assadi, Jiang and Xiang, closing the gap left by prior work.
Context
An established open question of the online-algorithms community; tight bounds for vertex cover under edge arrivals resisted a line of prior work.
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The authors had partial progress and suggested the Assadi-Jiang-Xiang blueprint might apply; "prompted by this suggestion, OpenAI's GPT-5.6 Sol formulated the reduction yielding the tight factor-2 lower bound proved in this paper and assisted with drafting the manuscript." The authors independently verified the reduction, proof and citations.
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