Parallel Computations in Graph Theory

In parallel computation two approaches are common, namely unbounded parallelism and bounded parallelism. In this paper both approaches will be considered with respect to graph theoretical algorithms. The problem of unbounded parallelism is studied in § 2 where some lower and upper bounds on different graph properties for directed and undirected graphs are presented. In § 3 we mention bounded parallelism and three different K-parallel graph search techniques, namely K-depth search, breadth-depth search, and breadth-first search. Each parallel algorithm is analyzed with respect to the optimal serial algorithm. It is shown that for sufficiently dense graphs the parallel breadth-first search technique is very close to the optimal bound.