Alessandro Arlotto, Robert W. Chen, Lawrence A. Shepp, J. Michael Steele
Published 2011-05-08, updated 2011-07-01Version 2
We consider sequential selection of an alternating subsequence from a sequence of independent, identically distributed, continuous random variables, and we determine the exact asymptotic behavior of an optimal sequentially selected subsequence. Moreover, we find (in a sense we make precise) that a person who is constrained to make sequential selections does only about 12% worse than a person who can make selections with full knowledge of the random sequence.
Journal: Journal of Applied Probability 48 (4), December 2011
Optimal On-Line Selection of an Alternating Subsequence: A Central Limit Theorem
A $O(\log n)$-optimal policy for the online selection of a monotone subsequence from a random sample
The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences
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