A Simultaneous Search Problem

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 [0, 1] with as little uncertainty as possible, using some given number k of probes. Each probe is specified by a real number r [0, 1]. After a probe at r, we are 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 k probes is 13 7 2-(k+1)/2 for odd k and 13 10 2-k/2 for even k. Key Words. Algorithm, Binary search, Probe model, Comparison model, Metrology.

• Type: Journal
• Year: 2000
• Where: ALGORITHMICA
• Authors: Ee-Chien Chang, Chee-Keng Yap
• Keywords: ALGORITHMICA 2000, Computational Metrology, Little Uncertainty, Unknown Numbers