New Effective Multithreaded Matching Algorithms

Matching is an important combinatorial problem with a number of applications in areas such as community detection, sparse linear algebra, and network alignment. Since computing optimal matchings can be very time consuming, several fast approximation algorithms, both sequential and parallel, have been suggested. Common to the algorithms giving the best solutions is that they tend to be sequential by nature, while algorithms more suitable for parallel computation give solutions of lower quality. We present a new simple 1/2-approximation algorithm for the weighted matching problem. This algorithm is both faster than any other suggested sequential 1/2-approximation algorithm on almost all inputs and when parallelized also scales better than previous multithreaded algorithms. We further extend this to a general scalable multithreaded algorithm that computes matchings of weight comparable with the best sequential deterministic algorithms. The performance of the suggested algorithms is documented through extensive experiments on different multithreaded architectures.