Finding Biconnected Components and Computing Tree Functions in Logarithmic Parallel Time (Extended Summary)

We propose a new algorithm for finding the blocks (biconnected components) of an undirected graph. A serial implementation runs in 0[n+m] time and space on a graph of n vertices and m edges. A parallel implmentation runs in 0[log n] time and 0[n+m] space using 0[n+m] processors on a concurrent-read, concurrent-write parallel RAM. An alternative implementation runs in 0[n/sup 2/p] time and 0[n/sup 2/] space using any number p ⩽ n/sup 2/log/sup 2/-n of processors, on a concurrent-read, exclusive-write parallel RAM. The latter algorithm has optimal speedup, assuming an adjacency matrix representation of the input. A general algorithmic technique which simplifies and improve computation of various functions on tress is introduced. This technique typically requires 0(log n) time using 0(n) space on an exclusive-read exclusive-write parallel RAM.

Authors

• Robert Endre Tarjan
• Uzi Vishkin

Keywords

• Concurrent computing
• Tree graphs
• Read-write memory
• Phase change random access memory
• Random access memory
• Computational modeling
• Writing
• Computer science
• US Department of Energy
• Parallel algorithms
• Input Representation
• Parallel Implementation
• Components Of The Graph
• Algorithmic Techniques
• Computational Model
• Implementation Of Algorithm
• Directed Graph
• Root Of The Tree
• Equivalence Relation
• Local Memory
• Parallel Algorithm
• Account In The Calculation
• Spanning Tree
• Sorting Algorithm
• Outgoing Edges
• Preorder
• Number Of Processors
• Path Tree
• Balanced Tree
• Edge Path
• Tree Edges