Combinatorial Optimization Reading Group - David Aleman

Title: Approximation Algorithms for Stochastic Knapsack 

Abstract: The classical Knapsack problem takes as input a set of items with some fixed nonnegative values and weights. The goal is to compute a subset of items of maximum total value, subject to the constraint that the total weight of these elements is at most a given limit. In this talk we review a paper by Gupta, Krishnaswamy, Molinaro and Ravi, in which the following stochastic variation of this problem is considered: the value and weight of each item are correlated random variables with known, arbitrary distributions. Items in the solution must be chosen sequentially, and once an item is chosen, its weight is instantiated. We will go over an LP based constant-factor approximation algorithm for this problem. This result generalizes a result of a paper by Dean, Goemans and Vondrak, discussed in a previous talk from the reading group, in which the stochastic Knapsack problem with deterministic values and random weights for the items was considered. If time permits, we will also look at the variation of the problem involving cancellations.