A study on the locality behavior of minimum spanning tree algorithms

Locality behavior study is crucial for achieving good performance for irregular problems. Graph algorithms with large, sparse inputs, for example, often times achieve only a tiny fraction of the potential peak performance on current architectures. Compared with most numerical algorithms graph algorithms lay higher pressure on the memory system. In this paper, using the minimum spanning tree problem as an example, we study the locality behavior of graph algorithms, both sequential and parallel, for arbitrary, sparse instances. We show that the inherent locality of graph algorithms may not be favored by the current architecture, and parallel graph algorithms tend to have significantly poorer locality behaviors than their sequential counterparts. As memory hierarchy gets deeper and processors start to contain multi-cores, our study suggests that architectural support and new parallel algorithm designs are necessary for achieving good performance for irregular graph problems.