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Computational Graph Theory pp 69–91Cite as

Basic Parallel Algorithms in Graph Theory

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Part of the book series: Computing Supplementum ((COMPUTING,volume 7))

Abstract

Basic Parallel Algorithms in Graph Theory. We discuss some of the more common machine models for parallel computation and their variants, as well as some relevant basic results from parallel complexity theory. We then describe a few of the very basic and fundamental “tricks” and techniques to obtain efficient parallel algorithms. Finally, we survey work on parallel algorithms for a number of graph theoretic problems.

AMS Subject Classifications: 68E10, 68Q10.

Zusammenfassung

Fundamentale Parallelalgoritbmeo in der Grapbeotbeorie. Wir diskutieren einige der gebrätuchlicheren Maschinenmodelle und ihre Varianten für Parallelrechnung, sowie einige wichtige und grundlegende Resultate aus der parallelen Komplexitätstheorie. Anschließend beschreiben wir eine Auswahl von elementaren und wichtigen “Tricks” und Methoden für effiziente parallele Algorithmen. Zum Schiuß geben wir einen Überblick über parallele Algorithmen für eine Reihe graphentheoretischer Probleme.

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References

  1. K. Abrahamson and N. Dadoun and D. G. Kirkpatrick and T. Przytycka. A simple parallel tree contraction algorithm. Technical Report 87–30, Department of Computer Science, University of British Columbia, Vancouver; August 1987.

    Google Scholar 

  2. A. Aggarwal and R. J. Anderson. A random NC algorithm for depth first search. Combinatorica, 8(1): 1–12, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Aggarwal and R. J. Anderson and M.-Y. Kao. Parallel depth-first search in general directed graphs. In Proceedings of the 21st Annual ACM Symposium on Theory of Computing (Seattle, Washington, May 15–17, 1989), pages 297–308, 1989.

    Google Scholar 

  4. A. V. Aho and J. E. Hopcroft and J. D. Ullman. The design and analysis of computer algorithms. Addison-Wesley 1974.

    MATH  Google Scholar 

  5. N. Alon and L. Babai and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. Algorithms, 7(4): 567–583, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Anderson and E. W. Mayr. Parallelism and the maximal path problem. Inf. Process. Lett., 24 (2): 121–126, 1987..

    Article  MathSciNet  MATH  Google Scholar 

  7. R. J. Anderson and G. L. Miller. Deterministic parallel list ranking. In Proceedings of the 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 88. Corfu, Greece, June/July 1988, pages 81–90, 1988.

    Google Scholar 

  8. Arvind, et al. The Tagged Token Date Flow Architecture. Technical Memo 229, Laboratory of Computer Science, MIT, 1983.

    Google Scholar 

  9. M. Atallah and U. Vishkin. Finding Euler tours in parallel. J. Comput. Syst. Sci., 29(3): 330–337, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  10. B. Awerbuch and A. Israeli and Y. Shiloach. Finding Euler circuits in logarithmic parallel time. In Proceedings of the 16th Ann. ACM Symposium on Theory of Computing (Washington, D. C), pages 249–257, 1984.

    Google Scholar 

  11. B. Awerbuch and Y. Shiloach. New connectivity and MSF algorithms for shuffle-exchange network and PRAM. IEEE Trans. Comput., C-36 (10): 1158–1163, 1987.

    Google Scholar 

  12. F. Bauernöppel and H. Jung. Fast parallel vertex colouring. In L. Budach, editor, Proceedings of the International Conference on Fundamentals of Computation Theory (Cottbus, GDR), pages 28–35. LNCS 199, Berlin, Heidelberg, New York, Tokyo: Springer-Verlag, 1985.

    Google Scholar 

  13. A. A. Bertpssi and M. A. Bonucelli. Some parallel algorithms on interval graphs. Discrete Appl. Math., 76: 101–111, 1987.

    Article  Google Scholar 

  14. A. Borodin. On relating time and space to size and depth. SIAM J. Comput, 6(4): 733–744, 1977.

    MathSciNet  MATH  Google Scholar 

  15. J. F. Boyar and H. J. Karloff. Coloring planar graphs in parallel. J. Algorithms, S(4):470–479, 1987.

    Article  MathSciNet  Google Scholar 

  16. A. Chandra, D. Kozen, and L. Stockmeyer. Alternation. J. ACM, 28(1): 114–133, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  17. A. K. Chandra and L. J. Stockmeyer and U. Vishkin. A complexity theory for unbounded fan-in parallelism. In Proceedings of the 23rd Ann. IEEE Symposium on Foundations of Computer Science (Chicago, IL), pages 1–13, 1982.

    Google Scholar 

  18. N. Chandrasekharan and S. S. Iyengar. NC algorithms for recognizing chordal graphs and k-trees. Technical Report 86–020, Department of Computer Science, Louisiana State University, 1986.

    Google Scholar 

  19. F. Y. Chin and J. Lam and I. Chen. Efficient parallel algorithms for some graph problems. Commun. ACM, 25(9): 659–665, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  20. M. Chrobak and M. Yung. Fast parallel and sequential algorithms for edge-coloring planar graphs (extended abstract). In J. H. Reif, editor, Proceedings of the 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 88. Corfu, Greece, June/July 1988, pages 11–23. LNCS 319, New York, Berlin, Heidelberg: Springer-Verlag, 1988.

    Google Scholar 

  21. R. Cole. Parallel merge sort. In Proceedings of the 27th Ann. IEEE Symposium on Foundations of Computer Science (Toronto, Canada), pages 511–516, 1986.

    Google Scholar 

  22. R. Cole and U. Vishkin. Deterministic coin tossing with applications to optimal parallel list ranking. Inf. Control, 70(1):32–53, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  23. R. Cole and U. Vishkin. Approximate and exact parallel scheduling with applications to list, tree, and graph problems. In Proceedings of the 27th Ann. IEEE Symposium on Foundations of Computer Science (Toronto, Canada), pages 478–491, 1986.

    Google Scholar 

  24. R. Cole and U. Vishkin. Optimal parallel algorithms for expression tree evaluation and list ranking. In Proceedings of the 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 88. Corfu, Greece, June/July 1988, pages 91–100 1988.

    Google Scholar 

  25. R. Cole and U. Vishkin. Faster optimal parallel prefix sums and list ranking. Inf. Comput., 81 (3): 334–352, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  26. E. Dahlhaus and M. Karpinski. The matching problem for strongly chordal graphs is in NC. Technical Report 855, Institut für Informatik, Universitat Bonn, 1986.

    Google Scholar 

  27. E. Dahlhaus and M. Karpinski. Parallel construction of perfect matchings and Hamiltonian cycles on dense graphs. Technical Report. Institut für Informatik, Universitat Bonn, 1987.

    Google Scholar 

  28. J. Dennis. Data Flow Supercomputers. Computer, 18:42–56, 1980.

    Google Scholar 

  29. D. M. Eckstein. Simultaneous memory access. Technical Report TR-79–6, Computer Science Department, Iowa State University, Ames, Iowa, 1979.

    Google Scholar 

  30. A. Edenbrandt. Chordal graph recognition is in NC. Inf. Process. Lett., 24: 239–241, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  31. S. Fortune and J. Wyllie. Parallelism in random access machines. In Proceedings of the 10th Ann. ACM Symposium on Theory of Computing (San Diego, CA), pages 114–118, 1978.

    Google Scholar 

  32. D. Fussel and V. Ramachandran and R. Thurimella. Finding triconnected components by local replacements. In G. Ausiello, M. Dezani-Ciancaglimi, S. Ronchi Delia Rocca, editors, Proceedings of the 16th International Colloquium on Automata, Languages and Programming (Stresa, Italy, July 1989), pages 379–393. LNCS 372, Berlin Heidelberg New York: Springer-Verlag, 1989.

    Chapter  Google Scholar 

  33. Z. Galil. Sequential and parallel algorithms for finding maximum matchings in graphs. Ann. Rev. Comput. Sci., 1: 197–224, 1986.

    Article  MathSciNet  Google Scholar 

  34. H. Gazit. An optimal randomized parallel algorithm for finding connected components in a graph. In Processings of the 27th Ann. IEEE Symposium on Foundations of Computer Science (Toronto, Canada), pages 492–501, 1986.

    Google Scholar 

  35. H. Gazit and G. L. Miller and S.-H. Teng. Optimal tree contraction in the EREW model. In Tewksbury, Stuart K. and Bradley W. Dickinson and Stuart C. Schwartz, editors, Concurrent Computations: Algorithms, Architecture, and Technology, pages 139–156, Plenum Press, 1988.

    Google Scholar 

  36. A. M. Gibbons and A. Israeli and W. Rytter. Parallel O(logn) time edge-colouring of trees and Halin graphs. Inf. Process. Lett., 27 (1): 43–51, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  37. A. Gibbons and W. Rytter. A fast parallel algorithm for optimal edge-colouring of outerplanar graphs. Research Report RR80, Department of Computer Science, University of Warwick, 1986.

    Google Scholar 

  38. A. Gibbons and W. Rytter. An optimal parallel algorithm for dynamic expression evaluation and its applications. In Proceedings of the Symposium on Foundations of Software Technology and Theoretical Computer Science, pages 453–469, 1986.

    Google Scholar 

  39. A. V. Goldberg and S. A. Plotkin. Parallel (Delta + l)-coloring of constant-degree graphs. Inf. Process. Lett., 25 (4): 241–245, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  40. A. Goldberg and S. Plotkin and G. Shannon. Parallel symmetry-breaking in sparse graphs. In Proceedings of the 19th Annual ACM Symposium on Theory of Computing (New York City, May 25–27, 1987), pages 315–324, 1987.

    Google Scholar 

  41. M. Goldberg and T. Spencer. A new parallel algorithm for the maximal independent set problem. SIAM J. Comput., 18 (2): 419–427, 1989.

    Article  MathSciNet  Google Scholar 

  42. L. Goldschlager. The monotone and planar circuit value problems are log-space complete for 8P. SIGACT News, 9 (2): 25–29, 1977.

    Article  Google Scholar 

  43. L. Goldschlager. A unified approach to models of synchronous parallel machines. In Proceedings of the 10th Ann. ACM Symposium on Theory of Computing (San Diego, CA), pages 89–94, 1978.

    Google Scholar 

  44. D. Y. Grigoriev and M. Karpinski. The matching problem for bipartite graphs with polynomially bounded permanents is in NC. In Proceedings of the 28th Ann. IEEE Symposium on Foundations of Computer Science (Los Angeles, CA, October 12–14, 1987), pages 166–172, 1987.

    Google Scholar 

  45. J. R. Guard and I. Watson and J. R. W. Glauert. A multi-layered data flow computer architecture. Technical Report, Univ. Manchester, 1978.

    Google Scholar 

  46. T. Hagerup and M. Chrobak and K. Diks. Optimal parallel 5-colouring of planar graphs. SIAM J. Comput., 18 (2): 288–300, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  47. X. He. Efficient parallel and sequential algorithms for 4-coloring perfect planar graphs. Technical Report 87–14, Department of Computer Science, State University of New York at Buffalo, 1987.

    Google Scholar 

  48. X. He and Y. Yesha. Parallel recognition and decomposition of two terminal series parallel graphs. Inf. Comput., 75 (1): 15–38, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  49. D. Helmbold and E. Mayr. Two processor scheduling is in NC. SIAM J. Comput., 16 (4): 747–759, 1987.

    Google Scholar 

  50. D. Helmbold and E. Mayr. Applications of parallel scheduling to perfect graphs. In Tinhofer, G., Schmidt, G., editors, Proceedings of the International Workshop WG ’86, Bernried, FRG, June 1986. Graph-Theoretic Concepts in Computer Science, pages 188–203. LNCS 246, Berlin Heidelberg: Springer-Verlag, 1987.

    Google Scholar 

  51. D. Helmbold and E. Mayr. Applications of parallel scheduling algorithms to families of perfect graphs. This issue

    Google Scholar 

  52. C. Hewitt and H. Baker. Laws for communicating parallel processes. AI Working Paper 134A, A. I. Laboratory, MIT, May 1977.

    Google Scholar 

  53. W. D. Hillis. The Connection Machine. MIT Press, Cambridge MA, 1985.

    Google Scholar 

  54. D. S. Hirschberg and A. K. Chandra and D. V. Sarwate. Computing connected components on parallel computers. Commun. ACM 22: 461–464, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  55. A. Israeli and A. Itai. A fast and simple randomized parallel algorithm for maximal matching. Inf. Process. Lett., 22 (2): 77–80, 1986.

    Article  MathSciNet  Google Scholar 

  56. A. Israeli and Y. Shiloach. An improved parallel algorithm for maximal matching. Inf. Process. Lett. 22 (2): 57–60, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  57. A. Kanevsky and V. Ramachandran. Improved algorithms for graph four-connectivity. In Proceedings of the 28th Ann. IEEE Symposium on Foundations of Computer Science (Los Angeles, CA, October 12–14, 1987), pages 252–259, 1987.

    Google Scholar 

  58. H. J. Karloff. A Las Vegas RNC algorithm for maximum matching. Combinatorica, 6(4): 387–392, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  59. H. J. Karloff and D. B. Shmoys. Efficient parallel algorithms for edge coloring problems. J. Algorithms, 8(1): 39–52, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  60. R. M. Karp and E. Upfal and A. Wigderson. Constructing a perfect matching is in random NC. Combinatorica, 6 (1): 35–48, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  61. R. M. Karp and A. Wigderson. A fast parallel algorithm for the maximal independent set problem. J. ACM, 32(4): 762–773, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  62. P. N. Klein. Efficient parallel algorithms for chordal graphs. In Proceedings of the 29th Ann. IEEE Symposium on Foundations of Computer Science (White Plains, NY, October 24–26, 1988), pages 150–161, 1988.

    Google Scholar 

  63. P. N. Klein and J. H. Reif. An efficient parallel algorithm for planarity. In Proceedings of the 27th Ann. IEEE Symposium on Foundations of Computer Science (Toronto, Canada), pages 465–477, 1986.

    Google Scholar 

  64. D. E. Knuth. The art of computer programming, Vol. 3: Sorting and searching. Addison-Wesley, Reading, MA, 1973.

    Google Scholar 

  65. S. R. Kosaraju and A. L. Delcher. Optimal parallel evaluation of tree-structured computations by ranking (extended abstract). In J. H. Reif, editor, Proceedings of the 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 88. Corfu, Greece, June/July 1988, pages 101–110. LNCS 319, New York, Berlin, Heidelberg: Springer-Verlag, 1988.

    Google Scholar 

  66. V. Koubek and J. Krsnakova. Parallel algorithms for connected components in a graph. In L. Budach, editor, Proceedings of the International Conference on Fundamentals of Computation Theory (Cottbus, GDR), pages 208–217. LNCS 199, Berlin, Heidelberg, New York, Tokyo: Springer- Verlag, 1985.

    Google Scholar 

  67. D. Kozen and U. V. Vazirani and V. V. Vazirani. NC algorithms for comparability graphs, interval graphs and testing for unique perfect matching. In Proceedings Fifth Conference on Foundations of Software Technology and Theoretical Computer Science, pages 496–503. LNCS 206, Berlin-Heidelberg-New York: Springer-Verlag,1985.

    Google Scholar 

  68. L. Kucera. Parallel computation and conflicts in memory access. Inf. Process. Lett., 14(2): 93–96, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  69. R. Ladner. The circuit value problem is log-space complete for P. SIGACT News, 7(1): 583–590, 1975.

    Article  MathSciNet  Google Scholar 

  70. R. Ladner and M. Fischer. Parallel prefix computation. J. ACM, 27(4): 831–838, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  71. C. E. Leiserson. Area-efficient graph layouts (for VLSI). In Proceedings of the 21st Ann. IEEE Symposium on Foundations of Computer Science, pages 270–281, 1980.

    Google Scholar 

  72. G. Lev and N. Pippenger and L. G. Valiant. A fast parallel algorithm for routing in permutation networks. IEEE Trans. Comput., C-30 (2): 93–100, 1981.

    MathSciNet  Google Scholar 

  73. L. Lovász. Computing ears and branchings in parallel. In Proceedings of the 26th Ann. IEEE Symposium on Foundations of Computer Science (Portland, OR), pages 464–467, 1985.

    Google Scholar 

  74. M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput., 5 (4): 1036–1042, 1986.

    Article  MathSciNet  Google Scholar 

  75. Y. Maon and B. Schieber and U. Vishkin. Parallel ear decomposition search (EDS) and stnumbering in graphs. Theor. Comput. Sci., 47 (3): 277–298, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  76. C. A. Mead and L. A. Conway. Introduction to VLSI systems. Reading, Mass.: Addison-Wesley, 1980.

    Google Scholar 

  77. R. Metcalfe and D. Boggs. Ethernet: Distributed packet switching for local computer networks. Commun. ACM, 79: 395–404. 1976.

    Article  Google Scholar 

  78. G. L.Miller and V. Ramachandran. Efficient parallel ear decomposition with applications. Manuscript, MSRI, Berkeley, 1986.

    Google Scholar 

  79. G. L. Miller and V. Ramachandran. A new graph triconnectivity algorithm and its parallelization. In Proceedings of the 19th Annual ACM Symposium on Theory of Computing (New York City, May 25–27, 1987), pages 335–344, 1987.

    Google Scholar 

  80. G. Miller and J. Reif. Parallel tree contraction and its application. In Proceedings of the 26th Ann. IEEE Symposium on Foundations of Computer Science (Portland, OR), pages 478–489. 1985.

    Google Scholar 

  81. A. Moitra and R. Johnson. Parallel algorithms for maximum matching and other problems on interval graphs. Technical Report 88–927, Department of Computer Science, Cornell University, 1988.

    Google Scholar 

  82. K. Mulmuley and U. V. Vazirani and V. V. Vazirani. Matching is as easy as matrix inversion. Combinatorica, 7 (1): 105–120, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  83. J. Naor. A fast parallel coloring of planar graphs with five colors. Inf. Process. Lett., 25 (1): 51–53, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  84. J. Naor and M. Naor and A. A. Schäffer. Fast parallel algorithms for chordal graphs. SIAM J. Comput, 18 (2): 327–349, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  85. D. Nath and S. N. Maheshwari. Parallel algorithms for the connected components and minimal spanning tree problems. Inf. Process. Lett., 74 (1): 7–11, 1982.

    Article  MathSciNet  Google Scholar 

  86. G. Pfister. The architecture of the IBM research parallel processor prototype (RP3). Technical Report RC 11210 Computer Science, IBM Yorktown Heights, 1985.

    Google Scholar 

  87. N. Pippenger. On simultaneous resource bounds. In Proceedings of the 20th Ann. IEEE Symposium on Foundations of Computer Science (San Juan, PR), pages 307–311, 1979.

    Google Scholar 

  88. V. Pratt and L. Stockmeyer. A characterization of the power of vector machines. J. Comput. Syst. Sci, 12: 198–221, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  89. F. Preparata and J. Vuillemin. The cube-connected-cycles: A versatile network for parallel computation. In Proceedings of the 20th Ann. IEEE Symposium on Foundations of Computer Science (San Juan, PR), pages 140–147, 1979.

    Google Scholar 

  90. V. Ramachandran. Fast parallel algorithms for reducible flow graphs. In Tewksbury, Stuart K. and Bradley W. Dickinson and Stuart C. Schwartz, editors, Concurrent Computations: Algorithms, Architecture, and Technology, pages 117–138, Plenum Press, 1988.

    Google Scholar 

  91. V. Ramachandran and U. Vishkin. Efficient parallel triconnectivity in logarithmic time (extended abstract). In J. H. Reif, editor, Proceedings of the 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 88. Corfu, Greece, June/July 1988, pages 33–42. LNCS 319, New York, Berlin, Heidelberg: Springer-Verlag, 1988.

    Google Scholar 

  92. J. H. Reif. Depth-first search is inherently sequential. Inf. Process. Lett., 20 (5): 229–234, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  93. W. L. Ruzzo. Tree-size bounded alternation. J. Comput. Syst. Sri., 21 (2): 218–235, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  94. W. L. Ruzzo. On uniform circuit complexity. J. Comput. Syst. Sci., 22 (3): 365–383, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  95. C. Savage and J. Ja’Ja. Fast efficient parallel algorithms for some graph problems. SIAM J. Comput., 10 (4): 682–691, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  96. B. Schieber and U. Vishkin. On finding lowest common ancestors: Simplification and parallelization (extended abstract). In J. H. Reif, editor, Proceedings of the 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 88. Corfu, Greece, June/July 1988, pages 111–123. LNCS 319, New York, Berlin, Heidelberg: Springer Verlag, 1988.

    Google Scholar 

  97. J. Schwartz. Ultracomputers. ACM Transactions on Programming Languages and Systems, 2 (4): 484–521, 1980.

    Article  MATH  Google Scholar 

  98. C. Seitz. The cosmic cube. CACM, 28(1): 22–33, 1985.

    MathSciNet  Google Scholar 

  99. H. J. Siegel. A model of SIMD machines and a comparison of various interconnection networks. IEEE Trans. Comput. C-28: 907–917, 1979.

    Article  Google Scholar 

  100. J. R. Smith. Parallel algorithms for depth-first searches. I Planar graphs. SIAM J. Comput., 15 (3): 814–830, 1986.

    MATH  Google Scholar 

  101. L. J. Stockmeyer and U. Vishkin. Simulation of parallel random access machines by circuits. SIAM J. Comput., 13 (2): 409–422, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  102. R. E. Tarjan. Efficiency of a good but not linear set union algorithm. J. ACM, 22: 215–225, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  103. R. E. Tarjan and U. Vishkin. An efficient parallel biconnectivity algorithm. SIAM J. Comput., 14 (4): 862–874, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  104. C. D. Thompson. Generalized connection networks for parallel processor interconnection. IEEE Trans. Comput, C-27: 1119–1125, 1978.

    Article  Google Scholar 

  105. Y. H. Tsin and F. Y. Chin. Efficient parallel algorithms for a class of graph theoretic problems. SIAM J. Comput, 13(3): 580–599, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  106. V. V. Vazirani. NC algorithms for computing the number of perfect matchings in K 3 3-free graphs and related problems. Technical Report, Computer Science Department, Cornell University, 1987.

    Google Scholar 

  107. U. Vishkin. Implementation of simultaneous memory address access in models that forbid it. J. Algorithms, 4 (1): 45–50, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  108. I. Wegener. The complexity of Boolean functions. Stuttgart: B. G. Teubner; New York: Wiley, 1987.

    Google Scholar 

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Authors and Affiliations

  1. Fachbereich Informatik, Johann Wolfgang Goethe-Univ., D-6000, Frankfurt a. M., Federal Republic of Germany

    Ernst W. Mayr

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  1. Ernst W. Mayr
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Editors and Affiliations

  1. Institut für Mathematik, Technische Universität München, Federal Republic of Germany

    G. Tinhofer

  2. Department of Computer Science, Stanford University, Calif., USA

    E. Mayr

  3. Institut für Informatik, Universität Würzburg, Federal Republic of Germany

    H. Noltemeier

  4. Institute of Computer Science, University of Wrocław, Poland

    M. M. Syslo

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Mayr, E.W. (1990). Basic Parallel Algorithms in Graph Theory. In: Tinhofer, G., Mayr, E., Noltemeier, H., Syslo, M.M. (eds) Computational Graph Theory. Computing Supplementum, vol 7. Springer, Vienna. https://doi.org/10.1007/978-3-7091-9076-0_4

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  • DOI: https://doi.org/10.1007/978-3-7091-9076-0_4

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