Theory and Applications of N-Fold Integer Programming

TL;DR

This paper introduces the theory of n-fold integer programming, providing polynomial time algorithms for complex linear and nonlinear integer problems, with applications in multicommodity flows and data privacy.

Contribution

It presents a new theoretical framework that enables polynomial time solutions for a broad class of integer programming problems.

Findings

First polynomial time algorithms for multicommodity flows

Polynomial algorithms for privacy in statistical databases

Unified theory for linear and nonlinear integer programming

Abstract

We overview our recently introduced theory of n-fold integer programming which enables the polynomial time solution of fundamental linear and nonlinear integer programming problems in variable dimension. We demonstrate its power by obtaining the first polynomial time algorithms in several application areas including multicommodity flows and privacy in statistical databases.