### Abstract

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 log_{2}n+E-log_{2}log_{2}n+O(E-Iog_{2}E) 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 log_{2}n+E-log_{2}log_{2}n+0(E-log_{2}E).

Original language | English (US) |
---|---|

Pages (from-to) | 227-232 |

Number of pages | 6 |

Journal | Proceedings of the Annual ACM Symposium on Theory of Computing |

DOIs | |

State | Published - May 1 1978 |

Event | 10th Annual ACM Symposium on Theory of Computing, STOC 1978 - San Diego, United States Duration: May 1 1978 → May 3 1978 |

### ASJC Scopus subject areas

- Software

### Cite this

*Proceedings of the Annual ACM Symposium on Theory of Computing*, 227-232. https://doi.org/10.1145/800133.804351

**Coping with errors in binary search procedures.** / Rivest, R. L.; Meyer, A. R.; Kleitman, D. J.; Winklmann, K.; Spencer, Joel.

Research output: Contribution to journal › Conference article

*Proceedings of the Annual ACM Symposium on Theory of Computing*, pp. 227-232. https://doi.org/10.1145/800133.804351

}

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, Joel

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).

UR - http://www.scopus.com/inward/record.url?scp=85053028262&partnerID=8YFLogxK

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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

ER -