Stochastic Packing Integer Programs with Few Queries

TL;DR

This paper introduces a framework for solving stochastic packing integer programs with limited queries by developing adaptive and non-adaptive algorithms, applicable to various combinatorial optimization problems.

Contribution

It presents a unified methodology for analyzing algorithms that efficiently handle stochastic objectives with few queries, advancing the solution of stochastic packing problems.

Findings

Framework applicable to matching, matroid, and stable set problems.

Provides performance analysis for adaptive and non-adaptive algorithms.

Demonstrates effectiveness in reducing queries while maintaining solution quality.

Abstract

We consider a stochastic variant of the packing-type integer linear programming problem, which contains random variables in the objective vector. We are allowed to reveal each entry of the objective vector by conducting a query, and the task is to find a good solution by conducting a small number of queries. We propose a general framework of adaptive and non-adaptive algorithms for this problem, and provide a unified methodology for analyzing the performance of those algorithms. We also demonstrate our framework by applying it to a variety of stochastic combinatorial optimization problems such as matching, matroid, and stable set problems.