Finding Euler tours in parallel
Journal of Computer and System Sciences
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
An improved parallel algorithm that computes the BFS numbering of a directed graph
Information Processing Letters
An O(n2 log n) parallel max-flow algorithm
Journal of Algorithms
All Graphs have Cycle Separators and Planar Directed Depth-First Search is in DNC
AWOC '88 Proceedings of the 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures
A Survey of Parallel Algorithms for Shared-Memory Machines
A Survey of Parallel Algorithms for Shared-Memory Machines
Graph Theory With Applications
Graph Theory With Applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A contraction procedure for planar directed graphs
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Efficient parallel shortest-paths in digraphs with a separator decomposition
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Graph-theoretic methods in database theory
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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Almost every problem on digraphs requires computing strongly connected components and directed spanning trees in one form or another. It has long been an open problem whether polylog time and linear processors are enough to find the strongly connected components of a digraph and compute directed spanning trees for these components. This paper provides the first non-trivial partial solution to this open problem: For a planar digraph with n vertices, the strongly connected components can be computed in O(log3n) time and O(n) processors. If the graph is strongly connected, a directed spanning tree can be built in O(log2 n) time and O(n) processors. Both algorithms are deterministic and run on a parallel random access machine that allows concurrent reads and concurrent writes in its shared memory.