TY - JOUR

T1 - Coping with errors in binary search procedures

AU - Rivest, R. L.

AU - Meyer, A. R.

AU - Kleitman, D. J.

AU - Winklmann, K.

AU - Spencer, J.

N1 - Funding Information:
This research was sponsored by NSF Grants MCS77-19754, MCS76-14294, and MCS77-19754A01 and ONR Grant NOOO-14-76-C-0036.
Publisher Copyright:
© 1978 Association for Computing Machinery. All rights reserved.

PY - 1978/5/1

Y1 - 1978/5/1

N2 - We consider the problem of identifying an unknown value xe{l, 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-Iog2E) 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).

AB - We consider the problem of identifying an unknown value xe{l, 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-Iog2E) 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).

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U2 - 10.1145/800133.804351

DO - 10.1145/800133.804351

M3 - Conference article

AN - SCOPUS:85053028262

SP - 227

EP - 232

JO - Proceedings of the Annual ACM Symposium on Theory of Computing

JF - Proceedings of the Annual ACM Symposium on Theory of Computing

SN - 0737-8017

T2 - 10th Annual ACM Symposium on Theory of Computing, STOC 1978

Y2 - 1 May 1978 through 3 May 1978

ER -