The parallel complexity of queue versus stack breadth-first search

Two algorithms for breadth-first search (BFS) are analyzed with respect to their parallel complexities. The stack (queue) BFS algorithm uses a stack (queue) as its underlying data structure. A natural decision problem based on stack BFS is proved P-complete, indicating the algorithm is inherently sequential. The proof technique used in the reduction is new. This theorem sharply contrasts a result the author presents showing that queue BFS is in NC, indicating the queue implementation is highly parallelizable. The significance of these results is due to the fundamental importance of BFS and due to their complementary nature