The weighted matching problem is to find a matching in a weighted graph that has maximum weight. The fastest known algorithm for this problem has running time O(nm + n2 log n). Many real world problems require graphs of such large size that this running time is too costly. We present a linear time approximation algorithm for the weighted matching problem with a performance ratio of 2/3-ε. This improves the previously best performance ratio of 1/2. © Springer-Verlag Berlin Heidelberg 2003.
Drake, D. E., & Hougardy, S. (2003). Improved linear time approximation algorithms for weighted matchings. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2764, 14–23. https://doi.org/10.1007/978-3-540-45198-3_2