# Probabilistic Analysis of Algorithms

Chapter

## Abstract

This paper is a brief introduction to the field of probabilistic analysis of algorithms; it is not a comprehensive survey. The first part of the paper examines three important probabilistic algorithms that together illustrate many of the important points of the field, and the second part then generalizes from those examples to provide a more systematic view.

## Keywords

Probabilistic Analysis Voronoi Diagram Sorting Algorithm Systematic View Probabilistic Algorithm
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

- [1]Bentley, J. L. [1979]. L. [1979]. “An introduction to algorithm design,” IEEE Comput. Magazine 12, February 1979, pp. 66–78.Google Scholar
- [2]Bentley, J. L. and M. I. Shamos [ 1978 ]. “Divide and conquer for linear expected time”, Inform. Process. Lett., 7, FebruaryGoogle Scholar
- [3]pp. 87–91.Google Scholar
- [4]Bentley, J. L., B. W. Weide and A. C. Yao [ 1980 ]. “Optimal expected-time algorithms for closest-point problems”, ACM Trans. Math. Software, 6, December 1980, pp. 563–580.Google Scholar
- [5] Devroye, L. [1979].Average time behavior of distributive sorting algorithms, Technical Report No. SOCS 79. 4, March 1979.Google Scholar
- [6]Floyd, R. W. and R. L. Rivest [ 1975 ]. “Expected time bounds for selection”, Comm. ACM, 18, March 1975, pp. 165–172.CrossRefGoogle Scholar
- [7]Hoare, C. A. R. [ 1962 ]. “Quicksort”, Comput. J.,.5, April 1962, pp. 10–15.Google Scholar
- [8]Janko, W. [ 1981 ]. “Bibliography of probabilistic algorithms”, in preparation.Google Scholar
- [9]Karp, R. M. [ 1977 ]. “Probabilistic analysis of partitioning algorithms for the traveling-salesman problem in the plane”, Math. Oper. Res., 2, August 1977, pp. 209–224.CrossRefGoogle Scholar
- [10]Linear expected-time algorithms for connectivity problems, J. Algorithms, JL, December 1980, pp. 374–393.Google Scholar
- [11]Knuth, D. E. [ 1973 ]. The Art of Computer Programming, volume 3: Sorting and Searching, Addison-Wesley, Reading, MA.Google Scholar
- [12]Knuth, D. E. [ 1980 ]. Class lecture in course Computer Science 255, Stanford University, March 1980.Google Scholar
- [13]Knuth, D. E. [ 1981 ]. The Art of Computer Programming, volume 2: Seminumerical Algorithms, Second Edition, Addison-Wesley, Reading, MA.Google Scholar
- [14]Lueker, G. [ 1979 ]. Optimization problems on graphs with independent random edge weights, UC-Irvine Technical Report #131, Department of Information and Computer Science.Google Scholar
- [15]Lueker, G. [ 1981 ]. “Algorithms with random inputs”, to appear in Proceedings of Computer Science and Statistics: Thirteenth Annual Symposium on the Interface, Pittsburgh, PA, March 1981.Google Scholar
- [16]Rabin, M. 0. [ 1976 ]. “Probabilistic algorithms”, Algorithms and Complexity: New Directions and Recent Results, J. F. Traub, Ed., Academic Press, New York, NY, pp. 21–39.Google Scholar
- [17]Rivest, R. L., A. Shamir and L. Adleman [ 1978 ]. “A method for obtaining digital signatures and public-key cryptosysterns”, Comm. ACM, 21, February 1978, pp. 120–126.CrossRefGoogle Scholar
- [19]Sedgewick, R. [ 1975 ], Quicksort, Stanford University Computer Science Department Report STAN-CS-75-492, May 1975.Google Scholar
- [19]Solovay, R. and V. Strassen [ 1977 ]. “A fast Monte-Carlo test for primality”, SIAM J. Comput., 6, March 1977, pp. 84–85.Google Scholar
- [20]Weide, B. W. [ 1978 ]. Statistical Methods in Algorithm Design and Analysis, Ph.D. Thesis, Carnegie-Mellon University, August 1978.Google Scholar
- [21]Yao, A. C. and F. F. Yao [ 1976 ]. “The complexity of searching an ordered random table”, Proceedings of the Seventeenth Annual Symposium on the Foundations of Computer Science, October 1976, IEEE, pp. 222–227.Google Scholar
- [AKLL79]R. Aleliunas, R. M. Karp, R. J. Lipton, and L. Lovasz (1979), “Random Walks, Universal Traversal Sequences, and the Complexity of Maze Problems,” Proceedings 20th Annual Symposium on Foundations of Computer Science, pp. 218–223.Google Scholar
- [AM77]L. Adleman and K. Manders (1977), “Reducibility, Randomness, and Intractibility,” Proceedings Ninth Annual ACM Symposium on Theory of Computing, pp. 151–163.Google Scholar
- [CW77]J. L. Carter and M. N. Wegman (1977), “Universal Classes of Hash Functions,” Proceedings Ninth Annual ACM Symposium on Theory of Computing, pp. 106–112.Google Scholar
- [De79]L. Devroye (1979), “Average Time Behavior of Distributive Sorting Algorithms,” Technical Report No. SOCS 79. 4.Google Scholar
- [ES74]P. Erdos and J. Spencer (1974), Probabilistic Methods in Combinatorics, Academic Press, New York.Google Scholar
- [Kn73]D. Knuth (1973), The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley, Reading, Mass.Google Scholar
- [Ra76]M. O. Rabin (1976), “Probabilistic Algorithms,” in Algorithms and Complexity: New Directions and Recent Results, J. F. Traub, ed., Academic Press, New York.Google Scholar
- [SS77]R. Solovay and V. Strassen (1977), “A Fast Monte-Carlo Test for Primality,” SIAM J. Comput., 6: 1, pp. 84–85.Google Scholar
- [We78]B. W. Weide (1978), Statistical Methods in Algorithm Design and Analysis, Ph.D. Thesis, Carnegie-Mellon University, Pittsburgh, Pennsylvania; appeared as CMU Computer Science Report CMU-CS-78-142.Google Scholar
- [Wi80]D. E. Willard (1982), “A Log Log N Search Algorithm for Nonuniform Distributions,” Proceedings of the Symposium on Applied Probability-Computer Science: The Interface, Birkhauser-Boston, Boston, MA.Google Scholar
- [Ya77]A. Yao (1977), “Probabilistic Computations: Toward a Unified Measure of Complexity,” Proceedings of the Eighteenth Annual Symposium on Foundations of Computer Science, pp. 222–227.Google Scholar

## Copyright information

© Birkhäuser Boston, Inc. 1982