Faster and simpler approximation of stable matchings

We give a 3/2-approximation algorithm for stable matchings that runs in $O(m)$ time. The previously best known algorithm by McDermid has the same approximation ratio but runs in $O(n^{3/2}m)$ time, where $n$ denotes the number of people and $m$ is the total length of the preference lists in a given instance. Also the algorithm and the analysis are much simpler. We also give the extension of the algorithm for the many-to-many setting. (This is the version of the paper from March 2011)