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The best choice problem for posets; colored complete binary trees

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  • Wojciech Kaźmierczak

    (Wrocław University of Technology)

Abstract

We consider the poset version of the secretary problem for rooted complete binary trees of a given length n where the $$2^{n-a}$$ 2 n - a complete binary trees whose roots are at the level $$a+1$$ a + 1 (counting from the leaves) are colored with different colors visible to the selector and the vertices above level $$a+1$$ a + 1 are colored in a natural way according to the vertices below them that came earlier. We find an optimal stopping time for two-colored trees and near optimal strategies for more than two colors.

Suggested Citation

  • Wojciech Kaźmierczak, 2016. "The best choice problem for posets; colored complete binary trees," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 13-28, January.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:1:d:10.1007_s10878-014-9705-5
    DOI: 10.1007/s10878-014-9705-5
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    References listed on IDEAS

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    1. D. V. Lindley, 1961. "Dynamic Programming and Decision Theory," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 10(1), pages 39-51, March.
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