A simultaneous search problem

E. C. Chang, Chee Yap

Research output: Contribution to journalArticle

Abstract

We introduce a new search problem motivated by computational metrology. The problem is as follows: we would like to locate two unknown numbers x, y ε [0, 1] with as little uncertainty as possible, using some given number k of probes. Each probe is specified by a real numbe r ε [0, 1]. After a probe at r, we arc told whether x ≤ r or x ≥ r, and whether y ≤ r or y ≥ r. We derive the optimal strategy and prove that the asymptotic behavior of the total uncertainty after it probes is 13/7 2 -(k+1)/2 for odd k and 13/10 2 -k/2 for even it.

Original languageEnglish (US)
Pages (from-to)255-262
Number of pages8
JournalAlgorithmica (New York)
Volume26
Issue number2
StatePublished - 2000

Fingerprint

Search Problems
Probe
Uncertainty
Optimal Strategy
Metrology
Arc of a curve
Odd
Asymptotic Behavior
Unknown

Keywords

  • Algorithm
  • Binary search
  • Comparison model
  • Metrology
  • Probe model

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Applied Mathematics
  • Safety, Risk, Reliability and Quality

Cite this

A simultaneous search problem. / Chang, E. C.; Yap, Chee.

In: Algorithmica (New York), Vol. 26, No. 2, 2000, p. 255-262.

Research output: Contribution to journalArticle

Chang, EC & Yap, C 2000, 'A simultaneous search problem', Algorithmica (New York), vol. 26, no. 2, pp. 255-262.
Chang, E. C. ; Yap, Chee. / A simultaneous search problem. In: Algorithmica (New York). 2000 ; Vol. 26, No. 2. pp. 255-262.
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