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Coping with Erroneous Information While Sorting
September 1991 (vol. 40 no. 9)
pp. 1081-1084

The authors study the problem of sorting n distinct elements in ascending sequence according to a total order, using comparison queries which receive 'yes' or 'no' answers, but of which as many as e may be erroneous. In a half-lie version, all 'yes' answers are guaranteed to be correct and the errors are confined to 'no' answers. It is shown that the comparison query complexity of the sorting problem for this case is Omega (n log n+e), and an asymptotically optimal algorithm is demonstrated. In a full-lie version, both 'yes' and 'no' answers can be false. It is shown that the comparison query complexity of the sorting problem for this case is Omega (n log n+en).

[1] T. H. Brylawski,"The mathematics of Watergate: An analysis of a two-party game," unpublished manuscript, 1977.
[2] A. Pelc, "Solution of Ulam's problem on searching with a lie,"J. Comb. Theory, Series A, vol. 44, no. 1, pp. 129-140, Jan. 1987.
[3] B. Ravikumar and K. B. Lakshmanan, "Coping with known patterns of lies in a search game,"Theoret. Comput. Sci., vol. 33, no. 1, pp. 85-94, Sept. 1984.
[4] B. Ravikumar, K. Ganesan, and K. B. Lakshmanan, "On selecting the largest element in spite of erroneous information," inProc. STACS 87, Lecture Notes in Computer Science, vol. 247. Berlin, Germany: Springer-Verlag, 1987, pp. 88-99.
[5] R. L. Rivest, A. R. Meyer, D. J. Kleitman, K. Winklmann, and J. Spencer, "Coping with errors in binary search procedures,"J. Comput. Syst. Sci., vol. 20, no. 3, pp. 396-404, June 1980.
[6] J. Spencer, "Guess a number--with lying,"Math. Mag., vol. 57, no. 2, pp. 105-108, Mar. 1984.
[7] S. M. Ulam,Adventures of a Mathematician. New York: Scribner, 1976.
[8] A. C. Yao and F. F. Yao, "On fault-tolerant networks for sorting,"SIAM J. Comput., vol. 14, no. 1, pp. 120-128, Feb. 1985.

Index Terms:
erroneous information; sorting; comparison queries; complexity; computational complexity; sorting.
Citation:
K.B. Lakshmanan, B. Ravikumar, K. Ganesan, "Coping with Erroneous Information While Sorting," IEEE Transactions on Computers, vol. 40, no. 9, pp. 1081-1084, Sept. 1991, doi:10.1109/12.83656
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