### Abstract

We consider the problem of identifying an unknown value x ε{lunate} {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 log_{2}n + E · log_{2}log_{2}n + O(E · log_{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 + O(E · log_{2}E).

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

Pages (from-to) | 396-404 |

Number of pages | 9 |

Journal | Journal of Computer and System Sciences |

Volume | 20 |

Issue number | 3 |

DOIs | |

State | Published - 1980 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Journal of Computer and System Sciences*,

*20*(3), 396-404. https://doi.org/10.1016/0022-0000(80)90014-8

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

Research output: Contribution to journal › Article

*Journal of Computer and System Sciences*, vol. 20, no. 3, pp. 396-404. https://doi.org/10.1016/0022-0000(80)90014-8

}

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.

PY - 1980

Y1 - 1980

N2 - We consider the problem of identifying an unknown value x ε{lunate} {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 + O(E · log2E).

AB - We consider the problem of identifying an unknown value x ε{lunate} {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 + O(E · log2E).

UR - http://www.scopus.com/inward/record.url?scp=0001328096&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001328096&partnerID=8YFLogxK

U2 - 10.1016/0022-0000(80)90014-8

DO - 10.1016/0022-0000(80)90014-8

M3 - Article

AN - SCOPUS:0001328096

VL - 20

SP - 396

EP - 404

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

SN - 0022-0000

IS - 3

ER -