Concurrent Disjoint Set Union

Bob Tarjan

The disjoint set union problem is a classical problem in data structures with a simple and efficient sequential solution that has a notoriously complicated analysis. One application is to find strongly connected components in huge, implicitly defined graphs arising in model checking. In this application, the use of multiprocessors has the potential to produce significant speedups. We explore this question. We devise and analyze wait-free concurrent implementations of standard sequential algorithms using single and double compare-and-swap primitives. We obtain work bounds that grow logarithmically with the number of processors, suggesting the possibility of significant speedup in practice. This is joint work with Siddhartha Jayanti.