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).
This work was funded by the Applied Mathematical Sciences program, U.S. Department of Energy, Office of Energy Research and performed at Sandia, a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the U.S. DOE under contract number DE-AC-94AL85000.
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References
A. Aggarwal and R. J. Anderson, A random NC algorithm for depth first search, Combinatorica, 8 (1988), pp. 1–12.
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.
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.
R. S. Baker and K. R. Koch, An S nalgorithm for the massively parallel CM-200 computer, Nuclear Science and Engineering, 128 (1998), pp. 312–320.
P. Chaudhuri, Finding and updating depth-first spanning trees of acyclic digraphs in parallel, The Computer Journal, 33 (1990), pp. 247–251.
R. Cole and U. Vishkin, Faster optimal prefix sums and list ranking, Information and Computation, 81 (1989), pp. 334–352.
T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, MIT Press and McGraw-Hill, Cambridge, MA, 1990.
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.
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.
T. Hagerup, Planar depth-first search in O(log n) parallel time, SIAM J. Comput., 19 (1990), pp. 678–704.
M.-Y. Kao, Linear-process or NG algorithms for planar directed graphs I: Strongly connected components, SIAM J. Comput., 22 (1993), pp. 431–459.
S. Pautz. Personal Communication, October 1999.
S. Plimpton. Personal Communication, May 1999.
J. H. Reif, Depth-first search is inherently sequential, Inform. Process. Lett., 20 (1985), pp. 229–234.
R. E. Tarjan, Depth first search and linear graph algorithms, SIAM J. Comput., 1 (1972), pp. 146–160.
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© 2000 Springer-Verlag Berlin Heidelberg
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Fleischer, L.K., Hendrickson, B., Pınar, A. (2000). On Identifying Strongly Connected Components in Parallel. In: Rolim, J. (eds) Parallel and Distributed Processing. IPDPS 2000. Lecture Notes in Computer Science, vol 1800. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45591-4_68
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DOI: https://doi.org/10.1007/3-540-45591-4_68
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