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Randomized parallel algorithms

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Solving Combinatorial Optimization Problems in Parallel

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1054))

Abstract

The opinion has sometimes been voiced that parallel randomized computations have only a pure theoretical interest. We instead believe that randomized algorithms have and will have several applications ranging from very theoretical to quite practical. The aim of this chapter has been to provide strong evidence of our convinction.

In our view the covered material represents only the starting point of a deeper study in the enourmous potentiality of probabilistic methods in the design and analysis of parallel algorithms. By the examples we have illustrated, readers from different research areas may find interesting ideas in their own topics.

This work was partially supported by the Human Capital and Mobility project SCOOP — Solving Combinatorial Optimization Problems in Parallel — of the European Union, and it was done when the first author had a Post-Doc Fellowship at the Centre Universitaire d'Informatique of University of Geneva.

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References

  1. N. Alon and J.H. Spencer: The Probabilistic Method. Wiley-Interscience Publication, 1992.

    Google Scholar 

  2. A. Aggarwal, R.J. Anderson: A Random NC Algorithm for Depth First Search. 19th Annual ACM-STOC, 325–334, 1987.

    Google Scholar 

  3. R.J. Anderson: A parallel algorithm for the maximal path problem. Combinatorica 7(3), 400–415, 1987.

    Google Scholar 

  4. L. Babai, Fortnow L. Levin L and M. Szegedy: Checking computation in polylogarithmic time. 23th Annual ACM-STOC 21–28, 1991.

    Google Scholar 

  5. B. Bollobas: Random Graphs. Academic Press, 1985.

    Google Scholar 

  6. D.P. Bovet and P. Crescenzi: Introduction to the Theory of Complexity. Prentice Hall, 1994.

    Google Scholar 

  7. A. Clementi, L. Kucera, J. Rolim: A Note on Parallel Randomized Algorithms for Searching Problems”, DIMACS Series in Discrete Mathematics and Theoretical Computer Sciences, American Mathematical Society, 22, 33–44, 1995.

    Google Scholar 

  8. E. Cohen: Polylog-time and near-linear work approximation scheme for undirected shortest paths. 26th Annual ACM-STOC, 16–26, 1994.

    Google Scholar 

  9. D. Coppersmith, P. Raghavan, M. Tompa: Parallel Graph Algorithms that are Efficient on Average. 28th Annual IEEE-FOCS, 260–269, 1987.

    Google Scholar 

  10. L. Csanky: Fast Parallel Matrix inversion Algorithms. SIAM J. of Computing 5, 618–623, 1976.

    Article  Google Scholar 

  11. P. Erdos and A. Renyi: On Random Graphs I. Publ. Math. Debrecen 6, 290–297, 1959.

    Google Scholar 

  12. L.R. Ford, D.R. Fulkerson: Flows in Networks. Princeton Univ. Press, Princeton, NJ, 1962.

    Google Scholar 

  13. Z. Galil, V. Pan: Improved Processor Bounds for Algebraic and Combinatorial Problems in RNC. 26th Annual IEEE-FOCS, 490–495, 1985.

    Google Scholar 

  14. M.R. Garey, D.S. Johnson: Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco, 1979.

    Google Scholar 

  15. R. K. Ghosh, G. P. Bhattacharjee: A parallel search algorithm for directed acyclic graphs. BIT 24, 134–150, 1984.

    Article  Google Scholar 

  16. R. Greenlaw: Polynomial Completeness and Parallel Computation. Synthesis of Parallel Algorithms, Ed. J. Reif, Morgan-Kaufmann, 1993.

    Google Scholar 

  17. J. Gil, Y. Matias, U. Vishkin: Towards a theory of nearly constant time parallel algorithms. 32th Annual IEEE-FOCS, 698–710, 1991.

    Google Scholar 

  18. J. JáJá: Parallel Algorithms. Addison-Wesley, 1992.

    Google Scholar 

  19. R. Karp: An introduction to randomized algorithms. Discr Appl Math, 34, 165–201, 1991.

    Article  Google Scholar 

  20. R.M. Karp, A. Wigderson: A fast parallel algorithm for the maximal independent set problem. J. of ACM, 32, 762–773, 1985.

    Article  Google Scholar 

  21. R.M. Karp, E. Upfal, A. Wigderson: Constructing a Maximum Matching is in Random NC. Combinatorica 6(1), 35–48, 1986. A preliminary version also appeared in 17th Annual ACM-STOC, 1985.

    Google Scholar 

  22. R. Karp and V. Ramachandran: Parallel Algorithms for Shared-Memory Machines. Handbook of T.C.S., Ed. J. van Leeuwen, Elsevier Science, Vol. A, Chapter 17, 1990.

    Google Scholar 

  23. P.N. Klein, S. Sairam: A Parallel Randomized Approximation Scheme for Shortest Paths. 24th Annual ACM-STOC, 750–758, 1992.

    Google Scholar 

  24. P.N. Klein, S. Sairam: A linear-processor polylog-time algorithm for shortest paths in planar graphs. Proc. of the 34th Annual IEEE FOCS 259–270, 1994.

    Google Scholar 

  25. D. Kavvadias, G.E. Pantziou, P.G. Spirakis, C. D. Zaroliagis: Hammock-on-Ears Decomposition: A Technique for the Efficient Parallel Solution of Shortest Paths and Other Problems. 19th MFCS, LNCS, 841, 462–472, 1994.

    Google Scholar 

  26. L. Kučera: Expected behaviour of graph coloring algorithms. Fundamentals in Computation Theory, LNCS, 56, 447–451, 1984.

    Google Scholar 

  27. L. Lovasz: On Determinants, Matchings and Random Algorithm. Fundamentals of Computing Theory, ed. L. Budach, Akademia-Verlag, Berlin, 1979.

    Google Scholar 

  28. M. Luby: A simple parallel algorithm for the maximal independent set problem. SIAM J. on Computing, 15, 1036–1053, 1986. (also in 17th Annual ACM-STOC).

    Article  Google Scholar 

  29. S. Micali V.V. Vazirani: An O(√¦V∥E¦) algorithm for finding maximum matching in general graphs. the 21st Annual Symp. on IEEE-FOCS. 17–27, 1980.

    Google Scholar 

  30. K. Mulmuley, U.V. Vazirani, V.V Vazirani: Matching is as easy as matrix inversion. Combinatorica 7, 105–113, 1987 (also in 19th Annual ACM-STOC, 345–354, 1987.

    Google Scholar 

  31. S. Nikoletseas, K. Palem, P. Spirakis, M. Yung: Short Vertex Disjoint paths and Multiconnectivity in Random Graphs: Reliable Networks Computing. 21st ICALP, LNCS, 508–519, 1994.

    Google Scholar 

  32. V. Pan: Fast and Efficient Algorithms for the Exact Inversion of Integer Matrices. Fifth Annual Foundations of Software Technology and Theoretical Computer Science Conference, pp. 504–521, 1985.

    Google Scholar 

  33. G. Pantziou, P. Spirakis and C. Zaroliagis: Coloring Random Graphs Efficiently in Parallel, through Adaptive Techniques. CTI TR-90.10.25, Comp. Techn. Institute, Patras. Also presented in the ALCOM Workshop on Graphs Algorithms, Data Structures and Computational Geometry, Berlin, October, 1990.

    Google Scholar 

  34. P. Raghavan, Motwani: Randomized Algorithms. Cambridge University Press, 1995.

    Google Scholar 

  35. P. Raghavan, C.D. Thompson: Provably good routing in graphs: regular arrays. 17th Annual ACM-STOC, 79–87, 1985.

    Google Scholar 

  36. E. Reghbati, D. Corniel: Parallel computations in graph theory. SIAM J. on Computing 7, 230–237, 1978.

    Article  Google Scholar 

  37. J. H. Reif: depth first search is inherently sequential. IPL 20, 229–234, 1985.

    Article  Google Scholar 

  38. J.T. Schwartz: Fast Probabilistic Algorithms for Verification of Polynomial Identities. J. of ACM 27(4), 701–717, 1980.

    Article  Google Scholar 

  39. M. Serna, P.G. Spirakis: Tight RNC Approximations to Max Flow. 8th Annual STACS, LNCS 480, 118–126, 1991.

    Google Scholar 

  40. J. R. Smith: Parallel algorithms for depth first searches I: planar graphs. SIAM J. on Computing 15(3), 814–830, 1986.

    Article  Google Scholar 

  41. W.T. Tutte: The Factorization of Linear Graphs. J. London Math. Soc. 22, pp. 107–111, 1947.

    Google Scholar 

  42. J. Ullmann, M. Yannakakis: High Probability parallel transitive closure algorithms. SIAM J. of Computing 20, 100–125, 1991.

    Article  Google Scholar 

  43. E. Urland: Experimental tests of efficient shortest paths heuristics for random graphs on the CM-2. Techn. Rep. 71, University of Geneva, August, 1994.

    Google Scholar 

  44. J. Van Leeuwen: Graph Algorithms, in Handbook of T.C.S. Ed. J. van Leeuwen, Elsevier Science, Vol. A, 10, 1990.

    Google Scholar 

  45. J.S. Vitter, P. Flajolet: Average-Case Analysis of Algorithms and Data Structures, in Handbook of T.C.S. Ed. J. van Leeuwen, Elsevier Science, Vol. A, 9, 1990.

    Google Scholar 

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Afonso Ferreira Panos Pardalos

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© 1996 Springer-Verlag Berlin Heidelberg

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Clementi, A., Rolim, J.D.P., Urland, E. (1996). Randomized parallel algorithms. In: Ferreira, A., Pardalos, P. (eds) Solving Combinatorial Optimization Problems in Parallel. Lecture Notes in Computer Science, vol 1054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027117

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  • DOI: https://doi.org/10.1007/BFb0027117

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