## Towards overcoming the transitive-closure bottleneck: efficient parallel algorithms for planar digraphs (1993)

Venue: | J. Comput. System Sci |

Citations: | 11 - 1 self |

### BibTeX

@ARTICLE{Klein93towardsovercoming,

author = {Philip N. Klein},

title = {Towards overcoming the transitive-closure bottleneck: efficient parallel algorithms for planar digraphs},

journal = {J. Comput. System Sci},

year = {1993}

}

### OpenURL

### Abstract

Abstract. 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 general 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.