The Bruss-Robertson Inequality: Elaborations, Extensions, and Applications
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sequential knapsack problem
sequential monotone subsequence problem
sequential selection
online selection
Markov decision problems
resource dependent branching processes
Bellman equation
Physical Sciences and Mathematics
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Abstract
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.