Abstract
The length of the longest monotone increasing subsequence of a random sample of size $n$ is known to have expected value asymptotic to $2n^{1/2}$. We prove that it is possible to make sequential choices which give an increasing subsequence of expected length asymptotic to $(2n)^{1/2}$. Moreover, this rate of increase is proved to be asymptotically best possible.
Citation
Stephen M. Samuels. J. Michael Steele. "Optimal Sequential Selection of a Monotone Sequence From a Random Sample." Ann. Probab. 9 (6) 937 - 947, December, 1981. https://doi.org/10.1214/aop/1176994265
Information