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Abstract

Randomness arises in connection with algorithms and their analysis in at least two different ways, Some algorithms (sometimes called coin-flipping algorithms) provide their own randomness, perhaps through the use of random number generators, Sometimes, though, it is useful to analyze the performance of a deterministic algorithm under some assumption about the distribution of inputs, We briefly survey some work which gives a perspective on such problems, Next we discuss some of the techniques which are useful when carrying out this type of analysis, Finally, we briefly discuss the problem of choosing an appropriate distribution

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References

  1. L. Adleman, “Two Theorems on Random Polynomial Time”, Proc. Nineteenth Annual Symposium on Foundations of Computer Science (1978), pp. 75–83.

    Google Scholar 

  2. L. Adleman, “On Distinguishing Prime Numbers from Composite Numbers”, Proc, 21stAnnualSymposiumonFoundationsofComputerScience (l980),pp. 387–406.

    Google Scholar 

  3. L. Adleman and K, Manders, “Reducibility,’Randomness, and Intractibility”, Proc, NinthAnnualACMSymposiumonTheoryofComputing (1977), pp. 151–163.

    Google Scholar 

  4. R. Aleliunas, R, M, Karp, R, J, Lipton, and L, Lovász, “Random Walks, Universal Traversal Sequences, and the Complexity of Maze Problems”, Proc, 20thAnnualSymposiumFoundationsofcomputer (1979), pp. 218–223.

    Google Scholar 

  5. J. L. Bentley, “Applications of Statistics in Applied Algorithm Design”, this Conference.

    Google Scholar 

  6. A. A. Borovkov, “A Probabilistic Formulation of Two Economic Problems”, Soviet Mathematics, 3:5 (1962), pp. 1403–1406.

    MathSciNet  Google Scholar 

  7. J. L. Carter and M. N. Wegman, “Universal Classes of Hash Functions”, Proc, Ninth Annual ACM Symposium on Theory of Computing (1977), pp. 106–112.

    Google Scholar 

  8. N. Christofides, Worst Case Analysis of New Heuristic for the Travelling Salesman Problem”, in Algorithms and Complexity: New Directions and Recent Results, J. F. Traub, ed., Academic Press, New York, 1976.

    Google Scholar 

  9. E. G. Coffman, Jr., K. So, M. Hofri, and A. C. Yao, “A Stochastic Model of Bin-Packing”, Information and Control 44:2 (February 1980), pp, 105–115.

    Article  MathSciNet  MATH  Google Scholar 

  10. S. A. Cook, “The Complexity of Theorem Proving Procedures”, Proc. Third Annual ACM Symposium on Theory of Computing (1971), pp. 151–158.

    Google Scholar 

  11. H. A. David, Order Statistics, John Wiley and Sons, New York, 1970.

    MATH  Google Scholar 

  12. L. Devroye, “Average Time Behavior of Distributive Sorting Algorithms”, Technical Report No. SOCS 79.4, March 1979.

    Google Scholar 

  13. L. Devroye, “On the Average Complexity of Various Sorting and Convex Hull Algorithms”, this conference.

    Google Scholar 

  14. W. E. Donath, “Algorithm and Average-value Bounds for Assignment Problems”, IBM J. Res. Dev. 13 (1969), pp. 380–386.

    Google Scholar 

  15. P. Erdös and A. Rényi, “On the Evolution of Random Graphs”, Publ. Math. Inst. Hung. Acad. Sci. 5A (1960), pp. 17–61.

    Google Scholar 

  16. P. Erdös and J Spencer, Probabilistic Methods in Combinatorics, Academic Press, New York, 1974.

    MATH  Google Scholar 

  17. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. I, Third Edition, John Wiley and Sons, New York, 1968.

    MATH  Google Scholar 

  18. William Feller, An Introduction to Probability Theory and Its Applications, Volume II, John Wiley and Sons, New York, 1966.

    Google Scholar 

  19. M. L. Fisher and D. S. Hochbaum, “Probabilistic Analysis of the Euclidean K-Median Problem”, Report 78–06–03, Wharton Department of Decision Sciences, University of Pennsylvania, May, 1978.

    Google Scholar 

  20. G. N. Frederickson, “Probabilistic Analysis for Simple One- and Two- Dimensional Bin Packing Algorithms”, Information Processing Letters 11:4,5 (12 December 1980), pp. 156–161.

    MathSciNet  Google Scholar 

  21. M. R. Garey and D. S. Johnson, “Approximation Algorithms for Combinatorial Problems: An Annotated Bibliography”, in Algorithms and Complexity: New Directions and Recent Results, J. F. Traub, ed., Academic Press, New York, 1976.

    Google Scholar 

  22. M. R. Garey and D. S. Johnson, “The Complexity of Near-Optimal Graph Coloring”, JACM 23:1 (January 1976), pp. 43–49.

    Article  MathSciNet  MATH  Google Scholar 

  23. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, San Francisco, 1979.

    Google Scholar 

  24. G. R. Grimmett and C. J. H. McDiarmid, “On Coloring Random Graphs”, Math. Proc. Camb. Phil. Soc. 77 (1975), pp. 313–324.

    Article  MathSciNet  MATH  Google Scholar 

  25. c. A. R. Hoare, “Algorithm 63: Quicksort”, CACM 4: 7 (July 1961), pp. 321–322.

    Google Scholar 

  26. O. H. Ibarra and C. E. Kim, “Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems”, JACM 22 (1975), pp. 463–468.

    Article  MathSciNet  MATH  Google Scholar 

  27. R. M. Karp, “Reducibility among Combinatorial Problems”, in Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, eds., Plenum Press, N. Y., 1972, pp. 85–104.

    Google Scholar 

  28. R. M. Karp, “Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane”, Math. Op. Res. 2:3 (August 1977), pp. 209–224.

    Article  MathSciNet  MATH  Google Scholar 

  29. R. M. Karp, “A Patching Algorithm for the Nonsymmetric Traveling-Salesman Problem”, SIAM J. Comput. 8:4 (November 1979), pp. 561–573.

    Article  MathSciNet  MATH  Google Scholar 

  30. D. Knuth. TheArtofComputerProgramming, Vol.3:SortingandSearching, Addison-Wesley, Reading, Mass., 1973.

    Google Scholar 

  31. G. S. Lueker, “On the Average Difference Between the Solutions to Linear and Integer Knapsack Problems”, Technical Report #152, Department of Information and Computer Science, University of California, Irvine, September 1980; presented at AppliedProbability--Computer Science,TheInterface, Boca Raton, Florida, January 1981.

    Google Scholar 

  32. G. S. Lueker, “Optimization Problems on Graphs with Independent Random Edge Weights”, Technical Report #131, Department of Information and Computer Science, University of California, Irvine; SIAMJ.Comput. to appear.

    Google Scholar 

  33. G. S. Lueker, “An Average-Case Analysis of Bin-Packing”, manuscript.

    Google Scholar 

  34. G. L. Miller, Riemann’s Hypothesis and Tests for Primality, Ph.D. Thesis, University of California at Berkeley, 1975.

    Google Scholar 

  35. M. O. Rabin, “Probabilistic Algorithms”, in Algorithms and Complexity: New Directions and Recent, J. F. Traub, ed., Academic Press, New York, 1976.

    Google Scholar 

  36. R. Rivest, A. Shamir, and L. Adleman, “A Method for Obtaining Digital Signatures and Public Key Cryptosystems”, CACM 21:2 (February 1978), pp. 120–126.

    MathSciNet  MATH  Google Scholar 

  37. R. Sedgewick, “Quicksort”, Report S-TAN-CS-75–492, Computer Science Department, Stanford University, May 1975.

    Google Scholar 

  38. R. Solovay and V. Strassen. “A Fast Monte-Carlo Test for Primality”, SIAM J. Comput. 6:1 (March 1977), pp. 84–85.

    Article  MathSciNet  MATH  Google Scholar 

  39. B. W. Weide, StatisticalMethodsinAlgorithmDesignandAnalysis, Ph.D. Thesis, Carnegie-Mellon University, pittsburgh, Pennsylvania (August 1978); appeared as CMU Computer Science Report CMU-CS-78–142.

    Google Scholar 

  40. D. E. Willard, “A Log Log N Search Algorithm for Nonuniform Distributions”, Applied Probability--Computer Science, the Interface, Boca Raton, Florida, 1981.

    Google Scholar 

  41. A. Yao. “Probabilistic Computations: Toward a Unified Measure of Complexity”, Proc. Eighteenth Annual Svmposium on Foundations of Computer Science (1977), pp. 222–227.

    Google Scholar 

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© 1981 Springer-Verlag New York Inc.

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Lueker, G.S. (1981). Algorithms with Random Input. In: Eddy, W.F. (eds) Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9464-8_11

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  • DOI: https://doi.org/10.1007/978-1-4613-9464-8_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90633-1

  • Online ISBN: 978-1-4613-9464-8

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