MPI-I-2004-1-002

We present two $\twothirds - \epsilon$ approximation algorithms for the maximum weight matching problem that run in time $O(m\log\frac{1}{\epsilon})$. We give a simple and practical randomized algorithm and a somewhat more complicated deterministic algorithm. Both algorithms are exponentially faster in terms of $\epsilon$ than a recent algorithm by Drake and Hougardy. We also show that our algorithms can be generalized to find a $1-\epsilon$ approximatation to the maximum weight matching, for any $\epsilon>0$.