Abstract
We present 0(log2n) step parallel algorithms for planarity testing and for finding the triply connected components of a graph. The algorithms use a polynomial number of synchronous processors with shared memory.
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Bibliography
Brent, R. P.: The Parallel Evaluation of General Arithmetic Expressions JACM 21 (1974) 201–206.
Bondy, J. A. and U. S. R. Murty: Graph Theory with Applications American Elsevier, NY (1977).
Csanky, L.: Fast Parallel Matrix Inversion Algorithms SIAM J. Comput. 5 (1976) 618–623.
Chandra, A. K.: Maximal Parallelism in Matrix Multiplication IBM Tech. Rept. RC 6193, Sept. 1976.
Flynn, M. J.: Very High-Speed Computing Systems Proc. IEEE 54 (Dec. 1976) 1901–1909.
Fortune, S. and J. Wyllie: Parallelism in Random Access Machines Proc. 10th Ann. ACM Symp. Comp. Th. Comp., San Diego, CA (1978) 114–118.
Goldschlager, C. M.: A Unified Approach to Models of Synchronous Parallel Machines Proc. 10th Ann. ACM Symp. Th. Comp., San Diego, CA (1978) 89–94.
Goldschlager, L. M.: Synchronous Parallel Computation TR 114 (1977) University of Toronto.
Harary, F.: Graph Theory Addison-Wesley, Reading, Mass. (1969).
Heller, D.: A Survey of Parallel Algorithms in Numerical Linear Algebra SIAM Review 20: 4 (1978) 740–777.
Hirschberg, D. S.: Parallel Algorithms for the Transitive Closure and the Connected Components Problems Proc. 8th Ann. ACM Symp. Th. Comp. (1976) 55–57.
Hartmanis, J. and J. Simon: On the Power of Multiplication in Random Access Machines Proc. 15th SWAT Conf., New Orleans, LA (1974) 13–23.
Ja'Ja', J: Graph Connectivity Problems on Parallel Computers Technical Report CS-78-05, Department of Computer Science, PSU, (Feb. 1978).
Ja'Ja', J. and J. Simon: Some Space-Efficient Algorithms Proc. 17th Allerton Conference, pp. 677–684, 1979.
McLane, S.: A Combinatorial Condition for Planar Graphs Fundamenta Math. 28 (1937) 22–32.
McLane, S.: A Structural Characterization of Planar Combinatorial Graphs Duke Math. J. 3 (1937) 46–472.
Preparata, F. P.: Parallelism in Sorting International Conference on Parallel Processing, Belair, Michigan (August 1977).
Pratt, V. R. and L. J. Stockmeyer: A Characterization of the Power of Vector Machines JCSS 12:2 (1976) 198–221.
Preparata, F. P. and D. V. Sarwate: An Improved Parallel Processor Bound in Fast Matrix Inversion IPL 7:3 (1978) 148–150.
Savage, C. and J. Ja'Ja': Fast, Efficient Parallel Algorithms for Some Graph Problems, submitted for publication.
Tutte, W. T.: How to Draw a Graph Proc. London Math. Soc. (3) 13 (1963) 743–768.
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Ja'Ja', J., Simon, J. (1980). Parallel algorithms in graph theory: Planarity testing (preliminary version). In: Dembiński, P. (eds) Mathematical Foundations of Computer Science 1980. MFCS 1980. Lecture Notes in Computer Science, vol 88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022513
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DOI: https://doi.org/10.1007/BFb0022513
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