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A Simultaneous Search Problem

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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 ∈ [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 \geq r , and whether y≤ r or y\geq 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 .

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Received November 11, 1996; revised October 2, 1997, and July 13, 1998.

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Chang, EC., Yap, C. A Simultaneous Search Problem . Algorithmica 26, 255–262 (2000). https://doi.org/10.1007/s004539910012

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  • DOI: https://doi.org/10.1007/s004539910012