### 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 language | English (US) |
---|---|

Pages (from-to) | 255-262 |

Number of pages | 8 |

Journal | Algorithmica (New York) |

Volume | 26 |

Issue number | 2 |

State | Published - 2000 |

### Fingerprint

### 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

*Algorithmica (New York)*,

*26*(2), 255-262.

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

Research output: Contribution to journal › Article

*Algorithmica (New York)*, vol. 26, no. 2, pp. 255-262.

}

TY - JOUR

T1 - A simultaneous search problem

AU - Chang, E. C.

AU - Yap, Chee

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

KW - Algorithm

KW - Binary search

KW - Comparison model

KW - Metrology

KW - Probe model

UR - http://www.scopus.com/inward/record.url?scp=8444246316&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=8444246316&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:8444246316

VL - 26

SP - 255

EP - 262

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 2

ER -