Linear-Time Approximation for Maximum Weight Matching

@article{Duan2014LinearTimeAF,
  title={Linear-Time Approximation for Maximum Weight Matching},
  author={Ran Duan and Seth Pettie},
  journal={J. ACM},
  year={2014},
  volume={61},
  pages={1:1-1:23}
}
The <i>maximum cardinality</i> and <i>maximum weight matching</i> problems can be solved in <i>Õ</i>(<i>m</i>√<i>n</i>) time, a bound that has resisted improvement despite decades of research. (Here <i>m</i> and <i>n</i> are the number of edges and vertices.) In this article, we demonstrate that this “<i>m</i>√<i>n</i> barrier” can be bypassed by approximation. For any <i>ε</i> > 0, we give an algorithm that computes a (1 − <i>ε</i>)-approximate maximum weight matching in <i>O</i>(<i>mε</i><sup… 

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