Data Structures and Algorithms

    

New Bounds for the Stochastic Knapsack Problem

Authors: Ekesh Kumar

The knapsack problem is a problem in combinatorial optimization that seeks to maximize an objective function subject to the a weight constraint. We consider the stochastic variant of this problem in which $\mathbf{v}$ remains deterministic, but $\mathbf{x}$ is an $n$-dimensional vector drawn uniformly at random from $[0, 1]^{n}$. We establish a sufficient condition under which the summation-bound condition is almost surely satisfied. Furthermore, we discuss the implications of this result on the deterministic problem.

Comments: 2 Pages.

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[v1] 2020-06-05 01:32:34

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