Coping with errors in binary search procedures

R. L. Rivest, A. R. Meyer, D. J. Kleitman, K. Winklmann, J. Spencer

Research output: Contribution to journalArticle

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 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).

Original languageEnglish (US)
Pages (from-to)396-404
Number of pages9
JournalJournal of Computer and System Sciences
Volume20
Issue number3
DOIs
StatePublished - Jun 1980

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

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