# 关于无意识匹配问题

In this paper, we propose the \textsf{Perturbed Greedy} algorithm for the edge-weighted oblivious matching problem and prove that it achieves a0.501approximation ratio. Besides, we show that the approximation ratio of our algorithm on unweighted graphs is0.639for bipartite graphs, and0.531for general graphs. The later improves the state-of-the-art result by Chan et al. (TALG 2018). Furthermore, our algorithm can be regarded as a robust version of the \textsf{Modified Randomized Greedy} (MRG) algorithm. By implication, our0.531approximation ratio serves as the first analysis of the MRG algorithm beyond the(1/2+ϵ)regime.

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