On selecting the largest element in spite of erroneous information

  • B. Ravikumar
  • K. Ganesan
  • K. B. Lakshmanan
Contributed Papers Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 247)


In this paper, we study the problem of finding the largest of a set of n distinct integers using comparison queries which receive “yes” or “no” answers, but some of which may be erroneous. If at most e queries can receive erroneous answers, we prove that (e+1)n−1 comparisons are necessary and sufficient to find the largest. If there is further restriction that errors are confined to “no” answers and that all “yes” answers are guaranteed to be correct, then 2n+2e−4 comparisons are sufficient. This contrasts with earlier results relating to errors in binary search procedures where both versions of the problem have the same complexity.


selection largest element comparisons errors lies adversary strategy analysis of algorithm selection networks 


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  1. [1]
    R.A. DeMillo, D.P. Dopkin, and R.J. Lipton, Combinatorial Inference, in Foundations of Secure Computation, R.A. DeMillo, D.P. Dopkin, A.K. Jones and R.J. Lipton, Eds., Academic Press, New York, 1978, pp.27–37.Google Scholar
  2. [2]
    G.O.H. Katona, Combinatorial Search Problems, in A Survey of Combinatorial Theory, J.N. Srivastava et al., Eds., North-Holland, Amsterdam, 1973, pp. 285–308.Google Scholar
  3. [3]
    B. Ravikumar, Coping With Errors in Searching, Selecting and Sorting, M.S. Thesis, Indian Institute of Technology, Madras, India, August 1983.Google Scholar
  4. [4]
    B. Ravikumar and K.B. Lakshmanan, Coping with Known Patterns of Lies in a Search Game, Theoretical Computer Science, Vol. 33, No.1, Sept. 1984, pp.85–94.Google Scholar
  5. [5]
    R.L. Rivest, A.R. Meyer, D.J. Kleitman, K. Winklman and J. Spencer, Coping with Errors in Binary Search Procedures, Journal of Computer and System Sciences, Vol. 20, No. 3, June 1980, pp. 396–404.Google Scholar
  6. [6]
    J.F. Traub, G.W. Wasilkowski and H. Wozniakowski, Information, Uncertainty, Complexity, Addison-Wesley, Reading, MA, 1983.Google Scholar
  7. [7]
    S.M. Ulam, Adventures of a Mathematician, Scribner, New York, 1976.Google Scholar
  8. [8]
    B. Weide, A Survey of Analysis Techniques for Discrete Algorithms, Computing Surveys, Vol.9, No.4, Dec. 1977, pp. 291–313.Google Scholar
  9. [9]
    A.C. Yao and F.F. Yao, On Fault-Tolerant Networks for Sorting, SIAM Journal of Computing, Vol.14, No.1, Feb. 1985, pp. 120–128.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • B. Ravikumar
    • 1
  • K. Ganesan
    • 2
  • K. B. Lakshmanan
    • 3
  1. 1.Department of Computer ScienceUniversity of MinnesotaMinneapolis
  2. 2.Department of Computer ScienceBoston UniversityBoston
  3. 3.Department of Computer Science and EngineeringIndian Institute of TechnologyMadrasIndia

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