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The Bruss-Robertson inequality gives a bound on themaximal number of elements of a random sample whose sum is less than a specifiedvalue, and the extension of that inequality which is given hereneither requires the independence of the summands nor requires the equality of their marginal distributions. A review is also given of the applications of the Bruss-Robertson inequality,especially the applications to problems of combinatorial optimization such as the sequential knapsack problem and the sequential monotone subsequence selection problem.
This work is licensed under a Creative Commons Attribution 3.0 License.
Order statistical inequalities, sequential knapsack problem, sequential monotone subsequence problem, sequential selection, online selection, Markov decision problems, resource dependent branching processes, Bellman equation
Steele, J. (2016). The Bruss-Robertson Inequality: Elaborations, Extensions, and Applications. Mathematica Applicanda, 44 (1), 3-16. http://dx.doi.org/10.14708/ma.v44i1.817
Date Posted: 27 November 2017
This document has been peer reviewed.