R. Rivest, A. Meyer, D. Kleitman, Karl Winklmann, J. Spencer
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Coping with errors in binary search procedures (Preliminary Report)
We consider the problem of identifying an unknown value x&egr;{1,2,...,n} using only comparisons of x to constants when as many as E of 'the comparisons may receive erroneous answers. For a continuous analogue of this problem we show that there is a unique strategy that is optimal in the worst case. This strategy for the continuous problem is then shown to yield a strategy for the original discrete problem that uses log2n+E.log2log2n+O(E.log2E) comparisons in the worst case. This number is shown to be optimal even if arbitrary “Yes-No” questions are allowed. We show that a modified version of this search problem with errors is equivalent to the problem of finding the minimal root of a set of increasing functions. The modified version is then also shown to be of complexity log2n+E.log2log2n+0(E.log2E).