Finding Biconnected Componemts And Computing Tree Functions In Logarithmic Parallel Time

  • Authors:
  • R. E. Tarjan;U. Vishkin

  • Affiliations:
  • AT&TBell Laboratories;-

  • Venue:
  • SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
  • Year:
  • 1984

Quantified Score

Hi-index 0.01

Visualization

Abstract

In this paper 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 /spl les/ 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.