Efficient Multi-core Algorithms for Computing Spanning Forests and Connected Components

The connected component and spanning tree problems fall into the category of graph problems where there is very little work compared to the amount of data. There exist a large number of PRAM algorithms for computing connected components and spanning trees; for a survey, see the paper by Bader and Cong. The OpenMP memory model allows for different threads to have conflicting views of the values of a variable residing in the shared memory as long as no flush directive has been issued. One of the more common uses of the Union-Find algorithm is in Kruskal’s algorithm for computing a minimum weight spanning tree. However, it should be possible to obtain a reasonable approximation to the minimum weight spanning tree by letting each processor process its own edges by increasing weight.