# On Identifying Strongly Connected Components in Parallel

Conference paper

First Online:

## Abstract

The standard serial algorithm for strongly connected components is based on depth first search, which is difficult to parallelize. We describe a divide-and-conquer algorithm for this problem which has significantly greater potential for parallelization. For a graph with *n* vertices in which degrees are bounded by a constant, we show the expected serial running time of our algorithm to be *O*(*n* log *n*).

## Keywords

Directed Graph Planar Graph Radiation Transport Discrete Ordinate Topological Sort
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## References

- 1.A. Aggarwal and R. J. Anderson,
*A random NC algorithm for depth first search*, Combinatorica, 8 (1988), pp. 1–12.zbMATHCrossRefMathSciNetGoogle Scholar - 2.A. Aggarwal, R. J. Anderson, and M.-Y. Kao,
*Parallel depth-first search in general directed graphs*, SIAM J. Comput., 19 (1990), pp. 397–409.zbMATHCrossRefMathSciNetGoogle Scholar - 3.D. A. Bader,
*A practical parallel algorithm for cycle detection in partitioned digraphs*, Tech. Rep. Technical Report AHPCC-TR-99-013, Electrical & Computer Eng. Dept., Univ. New Mexico, Albuquerque, NM, 1999.Google Scholar - 4.R. S. Baker and K. R. Koch,
*An S*_{n}*algorithm for the massively parallel CM-200 computer*, Nuclear Science and Engineering, 128 (1998), pp. 312–320.Google Scholar - 5.P. Chaudhuri,
*Finding and updating depth-first spanning trees of acyclic digraphs in parallel*, The Computer Journal, 33 (1990), pp. 247–251.CrossRefMathSciNetGoogle Scholar - 6.R. Cole and U. Vishkin,
*Faster optimal prefix sums and list ranking*, Information and Computation, 81 (1989), pp. 334–352.zbMATHCrossRefMathSciNetGoogle Scholar - 7.T. H. Cormen, C. E. Leiserson, and R. L. Rivest,
*Introduction to Algorithms*, MIT Press and McGraw-Hill, Cambridge, MA, 1990.Google Scholar - 8.M. R. Dorr and C. H. Still,
*Concurrent source iteration in the solution of 3-dimensional, multigroup discrete ordinates neutron-transport equations*, Nuclear Science and Engineering, 122 (1996), pp. 287–308.Google Scholar - 9.H. Gazit and G. L. Miller,
*An improved parallel algorithm that computes the BFS numbering of a directed graph*, Inform. Process. Lett., 28 (1988), pp. 61–65.zbMATHCrossRefMathSciNetGoogle Scholar - 10.T. Hagerup,
*Planar depth-first search in O*(log*n*)*parallel time*, SIAM J. Comput., 19 (1990), pp. 678–704.zbMATHCrossRefMathSciNetGoogle Scholar - 11.M.-Y. Kao,
*Linear-process or NG algorithms for planar directed graphs I: Strongly connected components*, SIAM J. Comput., 22 (1993), pp. 431–459.zbMATHCrossRefMathSciNetGoogle Scholar - 12.S. Pautz. Personal Communication, October 1999.Google Scholar
- 13.S. Plimpton. Personal Communication, May 1999.Google Scholar
- 14.J. H. Reif,
*Depth-first search is inherently sequential*, Inform. Process. Lett., 20 (1985), pp. 229–234.zbMATHCrossRefMathSciNetGoogle Scholar - 15.R. E. Tarjan,
*Depth first search and linear graph algorithms*, SIAM J. Comput., 1 (1972), pp. 146–160.zbMATHCrossRefMathSciNetGoogle Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 2000