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Integre Technical Publishing Co., Inc. Mathematics Magazine 84:1 November 10, 2010 2:08 p.m. notes.tex page 48 48 MATHEMATICS MAGAZINE
 

Summary: Integre Technical Publishing Co., Inc. Mathematics Magazine 84:1 November 10, 2010 2:08 p.m. notes.tex page 48
48 MATHEMATICS MAGAZINE
Other variants of the secretary problem were studied later for partial orders (com-
plete binary tree [7], general partial order [5, 8]), for graphs and digraphs [4], and
threshold stopping times [3].
The game described in this paper could be generalized to allow p different types of
elements, with p > 2. If the objective is to "choose rarity" by stopping on an element
in the smallest set, an optimal strategy seems to be analogous to the one described in
the paper, but finding probabilities of winning is more challenging.
REFERENCES
1. B. A. Berezovskiy and A. V. Gnedin, The Problem of Optimal Choice, Nauka, Moscow, 1984.
2. T. Ferguson, Who solved the secretary problem? Statist. Sci. 4 (1989) 282296. doi:10.1214/ss/
1177012493
3. A. V. Gnedin, Multicriteria extensions of the best choice problem: Sequential selection without linear order,
pp. 153172 in F. T. Bruss, T. S. Ferguson, and S. M. Samuels (eds.), Strategies for Sequential Search and
Selection in Real Time, American Mathematical Society, Providence, RI, 1992.
4. G. Kubicki and M. Morayne, Graph-theoretic generalization of the secretary problem; the directed path case,
SIAM J. Discrete Math. 19(3) (2005) 622632. doi:10.1137/S0895480104440596
5. M. Kuchta, M. Morayne, and J. Niemiec, On a universal best choice algorithm for partially ordered sets,
Random Structures Algorithms 32(3) (2008) 263273. doi:10.1002/rsa.20192

  

Source: Alperin, Roger C. - Department of Mathematics, San Jose State University

 

Collections: Mathematics