Breadth first search on massive graphs

We consider the problem of Breadth First Search (BFS) traversal on massive sparse undirected graphs. Despite the existence of simple linear time algorithms in the RAM model, it was considered non-viable for massive graphs because of the I/O cost it incurs. Munagala and Ranade [29] and later Mehlhorn and Meyer [27] gave efficient algorithms (refered to as MR BFS and MM BFS, respectively) for computing BFS level decompositions in an external memory model. Ajwani et al. [3] implemented MR BFS and the randomized variant of MM BFS using the external memory library STXXL and gave a comparative study of the two algorithms on various graph classes. In this paper, we review and extend that result demonstrating the effectiveness and viability of the BFS implementations on various other synthetic and real world benchmarks. Furthermore, we present the implementation of the deterministic variant of MM BFS and show that in most cases, it outperforms the randomized variant.