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arXiv · 2608.04994

A Tight Bound on Online Vertex Cover under Edge Arrivals

Zhihao Gavin Tang·Yuhao Zhang
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Abstract

We prove a tight impossibility result for online vertex cover under edge arrivals. No randomized integral or fractional algorithm achieves a competitive ratio strictly below $2$ against an oblivious adversary, even on bipartite graphs. Since the standard algorithm that takes both endpoints of every uncovered edge is $2$-competitive, this settles the optimal ratio. Our proof is a direct reduction from the recent breakthrough blueprint framework of Assadi, Jiang, and Xiang.

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Zhihao Gavin Tang, Yuhao Zhang. 2026-08-05. A Tight Bound on Online Vertex Cover under Edge Arrivals. https://arxiv.org/abs/2608.04994

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