Competitive ratio of online vertex cover
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In online vertex cover with edges arriving over time, is competitive ratio two unavoidable? The lower-bound target approaches 2 for deterministic fractional algorithms on finite bipartite instances and for randomized integral or fractional algorithms against an oblivious adversary.
Why it matters and what counts as progress
Why it matters: It asks whether the known upper ratio can be improved under the same edge-arrival information model.
What counts as progress: A matching lower bound approaching two for the stated edge-arrival model, including randomized algorithms against an oblivious adversary.
How the problem developed
- 2005 · Model study [1]
Online-algorithm researchers Studied online vertex covering under vertex-arrival and cluster-arrival models, distinguishing these from later edge-arrival formulations.
- 5 Aug 2026 · Lower bound [2]
Zhihao Gavin Tang and Yuhao Zhang Proved that no randomized integral or fractional algorithm beats competitive ratio 2 for edge-arrival bipartite vertex cover against an oblivious adversary; the standard algorithm attains 2.
AI contribution
A Tight Bound on Online Vertex Cover under Edge Arrivals
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
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Publication dates and editorial changes.
AI-suggested reduction makes the online vertex-cover bound tight