Optimal sequential and parallel seach for finding a root

Shmuel Gal, Willard Miranker

Research output: Contribution to journalArticlepeer-review


Given n opportunities to evaluate a function which is known to have a root in the unit interval, how should these evaluations be used to specify the smallest possible interval containing that root? If f(x) is continuous the answer is the well-known method of binary search and the smallest interval has length ( 1 2)n. The authors solve this optimal search problem in the case of a sequential and a parallel search for the class of functions whose divided differences are bounded above by a number M and below by a number m (m > 0). It is shown that in the sequential case the best interval has length { 1 2[1 - ( m M)]}n. For the optimal search in the parallel case r parallel evaluations are shown to be equivalent to approximately 1 + log r sequential evaluations.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalJournal of Combinatorial Theory. Series A
Issue number1
StatePublished - Jul 1977
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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