Towards overcoming the transitive-closure bottleneck: efficient parallel algorithms for planar digraphs

M.-Y. Kao, P. N. Klein
1990 Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90  
Currently, there is a significant gap between the best sequential and parallel complexities of many fundamental problems related to digraph reachability. This complexity bottleneck essentially reflects a seemingly unavoidable reliance on transitive closure techniques in parallel algorithms for digraph reachability. To pinpoint the nature of the bottleneck, we de* velop a collection of polylog-time reductions among reachability problems. These reductions use only linear processors and work for
more » ... neral graphs. Furthermore, for planar digraphs, we give polylog-time algorithms for the following problems: (1) directed ear decomposition, (2) topological ordering, (3) digraph reachability, (4) descendent counting, and (5) depth-first search. These algorithms use only linear processors and therefore reduce the complexity to within a polylog factor of optimal.
doi:10.1145/100216.100237 dblp:conf/stoc/KaoK90 fatcat:fvdrufhpvfgxdmm6yuu7dezemy