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Introduction to special issue on randomized and derandomized algorithms

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References

  1. N. Alon, L. Babai, A. Itai, A fast and simple randomized parallel algorithm for the maximal independent set problem,Journal of Algorithms, 1986, Vol. 7, pp. 567–583.

    Google Scholar 

  2. N. Alon, O. Goldreich, J. Håstad, R. Peralta, Simple constructions of almostk-wise independent random variables,Random Structures and Algorithms, 1992, Vol. 3, No. 3, pp. 289–304. (See also addendum inRandom Structures and Algorithms, 1993, Vol. 4, No. 1, pp. 119–120.)

    Google Scholar 

  3. N. Alon, M. Naor, Derandomization, witnesses for Boolean matrix multiplication and construction of perfect hash functions, this issue.

  4. H. Alt, L. Guibas, K. Mehlhorn, R. Karp, A. Wigderson, A method for obtaining randomized algorithms with small tail probabilities, this issue.

  5. Y. Azar, A. Broder, A. Karlin, E. Upfal, Balanced allocations,Proceedings of the 26th Annual ACM Symposium on Theory of Computing, May 1994, pp. 593–602.

  6. B. Berger, J. Rompel, Simulating (Iogc n)-wise independence inNC, Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science, 1989, pp. 1–7.

  7. M. Blum, Independent unbiased coin flips from a correlated biased source: a finite Markov chain,Combinatorica, 1986, Vol. 6, No. 2, pp. 97–108.

    Google Scholar 

  8. A. Broder, How hard is it to marry at random (on the approximation of the permanent),Proceedings of the 18th Annual ACM Symposium on Theory of Computing, May 1986, pp. 50–58.

  9. J. Carter, M. Wegman, Universal classes of hash functions,Journal of Computer and System Sciences, 1979, Vol. 18, pp. 143–154.

    Google Scholar 

  10. B. Chazelle, J. Matoušek, On linear-time deterministic algorithms for optimization problems in fixed dimensions,Proceedings of the 4th SIAM-ACM Symposium on Discrete Algorithms, 1993, pp. 281–290.

  11. B. Chor, O. Goldreich, Unbiased bits from sources of weak randomness and probabilistic communication complexity,SIAM Journal on Computing, 1988, Vol. 17, No. 2, pp. 230–261.

    Google Scholar 

  12. B. Chor, O. Goldreich, On the power of two point based sampling,Journal of Complexity, 1989, Vol. 5, pp. 96–106.

    Google Scholar 

  13. K. Clarkson, Linear programming inO(n · 3d 2) time,Information Processing Letters, 1986, Vol. 22, pp. 21–24.

    Google Scholar 

  14. K. Clarkson, Las Vegas algorithms for linear and integer programming when the dimension is small,Proceedings of the 29th IEEE Symposium on Foundations of Computer Science, 1988, pp. 452–457.

  15. P. Dagum, R. Karp, M. Luby, S. Ross, An optimal algorithm for Monte Carlo estimation,Proceedings of 36th Annual IEEE Symposium on Foundations of Computer Science, 1995, pp. 142–149.

  16. P. Dagum, M. Luby, Approximating the permanent of graphs with large factors,Theoretical Computer Science, 1992, Part A, Vol. 102, pp. 283–305.

    Google Scholar 

  17. P. Dagum, M. Luby, M. Mihail, U. Vazirani, Polytopes, permanents and graphs with large factors,Proceedings of the 29th Annual IEEE Symposium on Foundations of Computer Science, 1988, pp. 412–421.

  18. D. Danzig,Linear Programming and Extensions, Princeton University Press, Princeton, NJ, 1963.

    Google Scholar 

  19. M. Dietzfelbinger, A. Karlin, K. Mehlhorn, F. Meyer auf der Heide, H. Rohnert, R. E. Tarjan, Dynamic Perfect Hashing: Upper and Lower Bounds, Technical Report 77, FB Mathematik-Informatik, Universität-GH Paderborn, Jan. 1991. (Revised version of paper with same title that appeared inProceedings of the 24th IEEE Symposium on Foundations of Computer Science, pp. 524–531, 1988).SIAM Journal on Computing, 1994, Vol. 23, No. 4, pp. 738–761.

    Google Scholar 

  20. M. Dietzfelbinger, F. Meyer auf der Heide, A new universal class of hash functions and dynamic hashing in real time,Proceedings of the 17th International Colloquium on Algorithms and Logic Programming, M. S. Paterson, ed., Lecture Notes in Computer Science, Vol. 443, Springer-Verlag, Berlin, 1990, pp. 6–19.

    Google Scholar 

  21. M. Dyer, On a multidimensional search technique and its applications to the Euclidean one-center problem,SIAM Journal on Computing, 1986, Vol. 15, pp. 725–738.

    Google Scholar 

  22. M. Dyer, A. Frieze, A randomized algorithm for fixed-dimensional linear programming,Mathematical Programming, 1989, Vol. 44, pp. 203–212.

    Google Scholar 

  23. M. Dyer, A. Frieze, R. Kannan, A random polynomial time algorithm for approximating the volume of convex bodies,Proceedings of the 21st Annual ACM Symposium on Theory of Computing, 1989, pp. 375–381.

  24. M. Dyer, A. Frieze, R. Kannan, A. Kapoor, L. Kerkovic, U. Vazirani, A mildly exponential time algorithm for approximating the number of solutions to a multidimensional knapsack problem,Combinatorics, Probability and Computing, 1993, Vol. 2, pp. 271–284.

    Google Scholar 

  25. P. Elias, The efficient construction of an unbiased random source,Annals of Mathematical Statistics, 1972, Vol. 43, No. 3, pp. 865–870.

    Google Scholar 

  26. W. Ertel, M. Luby, Optimal parallelization of Las Vegas algorithms,Proceedings of the Symposium on Theoretical Aspects of Computer Science, Lecture Note in Computer Science, Vol. 775, Springer-Verlag, Berlin, 1994, pp. 463–475.

    Google Scholar 

  27. G. Even, O. Goldreich, M. Luby, N. Nisan, B. Veličković, Approximations of general independent distributions,Proceedings of the 24th Annual ACM Symposium on Theory of Computing, 1992, pp. 10–16.

  28. J. Gil, Y. Matias. Fast hashing on a PRAM-designing by expectation,Proceedings of the SIAM-ACM Symposium on Discrete Algorithms, 1991, pp. 271–280.

  29. M. Jerrum, A. Sinclair, Approximating the permanent,SIAM Journal on Computing, 1989, Vol. 18, pp. 1149–1178.

    Google Scholar 

  30. M. Jerrum, A. Sinclair, Polynomial-time approximation algorithms for the Ising model,SIAM Journal on Computing, 1993, Vol. 22, pp. 1087–1116.

    Google Scholar 

  31. M. Jerrum, U. Vazirani, A mildly exponential approximation algorithm for the permanent, this issue.

  32. G. Kalai, A subexponential randomized simplex algorithm,Proceedings of the 24th Annual ACM Symposium on Theory of Computing, 1992, pp. 475–482.

  33. H. Karloff, P. Raghavan, Randomized algorithms and pseudorandom numbers,Journal of the Association for Computing Machinery, 1993, Vol. 40, pp. 421–453.

    Google Scholar 

  34. N. Karmarkar, A new polynomial-time algorithm for linear programming,Combinatorica, 1984, Vol. 4, pp. 373–395.

    Google Scholar 

  35. N. Karmarkar, R. Karp, R. Lipton, L. Lovász, M. Luby, A Monte-Carlo algorithm for estimating the permanent,SIAM Journal on Computing, 1993, Vol. 22, No. 2, pp. 284–293.

    Google Scholar 

  36. R. Karp, M. Luby, Monte-Carlo algorithms for enumeration and reliability problems,Proceedings of the 24th Annual ACM Symposium on Theory of Computing, 1983, pp. 56–64.

  37. R. Karp, M. Luby, N. Madras, Monte-Carlo approximation algorithms for enumeration problems,Journal of Algorithms, 1989, Vol. 10, No. 3, pp. 429–448.

    Google Scholar 

  38. R. Karp, M. Luby, F. Meyer auf der Heide, Efficient PRAM simulation on a distributed memory machine, this issue.

  39. R. Karp, A. Wigderson, A fast parallel algorithm for the maximal independent set problem,Proceedings of the 16th ACM Symposium on Theory of Computing, 1984, pp. 266–272.

  40. M. Karpinski, M. Luby, Approximating the number of solutions to aGF[2] formula,Journal of Algorithms, 1993, Vol. 14, No. 2, pp. 280–287.

    Google Scholar 

  41. C. Kenyon, D. Randall, A. Sinclair, Matchings in lattice graphs,Proceedings of the 25th Annual ACM Symposium on Theory of Computing, May 1993, pp. 738–746. Journal version: Approximating the number of monomer-dimer coverings of a lattice,Journal of Statistical Physics, 1996, Vol. 83, pp. 637–659.

  42. L. Khachiyan. Polynomial algorithm in linear programming,U.S.S.R. Computational Mathematics and Mathematical Physics, 1980, Vol. 20, pp. 53–72.

    Google Scholar 

  43. N. Linial, M. Luby, M. Saks, D. Zuckerman, Efficient construction of a small hitting set for combinatorial rectangles in high dimension,Proceedings of the 25th Annual ACM Symposium on Theory of Computing, 1993, pp. 258–267.

  44. M. Luby, A simple parallel algorithm for the maximal independent set problem,SIAM Journal on Computing, 1986, Vol. 15, No. 4, pp. 1036–1053

    Google Scholar 

  45. M. Luby, Removing randomness in parallel computation without a processor penalty,Journal of Computer and System Sciences, 1993, Vol. 47, No. 2, pp. 250–286.

    Google Scholar 

  46. M. Luby, A. Sinclair, D. Zuckerman, Optimal speedup of Las Vegas algorithms,Information Processing Letters, 1993, Vol. 47, pp. 173–180.

    Google Scholar 

  47. M. Luby, B. Veličković, On deterministic approximation of DNF, this issue.

  48. M. Luby, B. Veličković, A. Wigderson, Deterministic approximate counting of depth-2 circuits,Proceedings of the Second Israeli Symposium on Theory of Computing and Systems, 1993, pp. 18–24.

  49. Y. Matias, U. Vishkin. Converting high probability into nearly-constant time—with applications to parallel hashing.Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, 1991, pp. 307–316.

  50. J. Matoušek, M. Sharir, E. Welzl, A subexponential bound for linear programming, this issue.

  51. N. Megiddo. Linear programming in linear time when the dimension is fixed,Journal of the Association for Computing Machinery, 1984, Vol. 31, pp. 114–127.

    Google Scholar 

  52. M. Mihail, P. Winkler, On the number of Eulerian orientations of a graph, this issue.

  53. R. Motwani, J. Naor, M. Naor, The probabilistic method yields parallel deterministic algorithms,Journal of Computer and System Sciences, 1994, Vol. 49, pp. 478–516.

    Google Scholar 

  54. K. Mulmuley, Randomized geometric algorithms and pseudorandom generators, this issue.

  55. M. Naor, S. Naor, Small bias probability spaces: Efficient constructions and applications,Proceedings of the 22nd Annual ACM Symposium on the Theory of Computing, 1990, pp. 213–223.

  56. J. von Neumann,Various Techniques Used in Connection with Random Digits, Notes by G. E. Forsythe, National Bureau of Standards, Applied Mathematic Series, Vol. 12, Pitmar, Boston, MA, 1951, pp. 36–38.

    Google Scholar 

  57. H. Ryser,Combinatorial Mathematics, The Carus Mathematical Monographs, No. 14, Mathematical Association of America, Washington, DC, 1963.

    Google Scholar 

  58. M. Santha, U. Vazirani, Generating quasi-random sequences from semi-random sources,Journal of Computer and System Sciences, 1986, Vol. 33, No. 1, pp. 75–87.

    Google Scholar 

  59. R. Seidel, Low dimensional linear programming and convex hulls made easy,Discrete & Computational Geometry, 1991, Vol. 6, pp. 423–434.

    Google Scholar 

  60. R. Seidel, C. R. Aragon, Randomized search trees, this issue.

  61. A. Siegel, On universal classes of fast high performance hash functions, their time-space tradeoff, and their applications,Proceedings of the 30th IEEE Annual Symposium on Foundations of Computer Science, 1989, pp. 20–25.

  62. L. Valiant, The complexity of enumeration and reliability problems,SIAM Journal on Computing, Vol. 8, 1979, pp. 410–421.

    Google Scholar 

  63. U. Vazirani, Efficiency considerations in using semi-random sources,Proceedings of the 19th Annual ACM Symposium on Theory of Computing, May 1987, pp. 160–168.

  64. U. Vazirani, V. Vazirani, Random polynomial time is equal to semi-random polynomial time,Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science, 1985, pp. 417–428.

  65. A. Wigderson, Improving the performance guarantee for approximate graph coloring,Journal of the Association for Computing Machinery, 1983, Vol. 30, No. 4, pp. 729–735.

    Google Scholar 

  66. D. Zuckerman, Simulating BPP using a general weak random source, this issue.

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Research partially supported by National Science Foundation Operating Grant CCR-9016468, National Science Foundation Operating Grant CCR-9304722, United States-Israel Binational Science Foundation Grant No. 89-00312, United States-Israel Binational Science Foundation Grant No. 92-00226, and ESPRIT BR Grant EC-US 030.

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Luby, M. Introduction to special issue on randomized and derandomized algorithms. Algorithmica 16, 359–366 (1996). https://doi.org/10.1007/BF01940869

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