Stochastic Combinatorial Optimization under Probabilistic Constraints

TL;DR

This paper develops approximation algorithms for stochastic combinatorial optimization problems with probabilistic constraints, focusing on the k-center and set cover problems under product distributions and different adaptive settings.

Contribution

It introduces novel approximation algorithms for probabilistic constraints in stochastic combinatorial optimization, addressing both adaptive and non-adaptive scenarios with product distributions.

Findings

Efficient approximation algorithms for probabilistic constraints.

Applicable to k-center and set cover problems.

Addresses both adaptive and non-adaptive settings.

Abstract

In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center problem and the set cover problem, with uncertainty characterized by a probability distribution over set of points or elements to be covered. We consider these problems under adaptive and non-adaptive settings, and present efficient approximation algorithms for the case when underlying distribution is a product distribution. In contrast to the expected cost model prevalent in stochastic optimization literature, our problem definitions support restrictions on the probability distributions of the total costs, via incorporating constraints that bound the probability with which the incurred costs may exceed a given threshold.