Protection of flows under targeted attacks

TL;DR

This paper introduces a new polynomial-time solvable robust maximum flow model that defends against targeted attacks, applicable to various network routing problems, and explores extensions with protection budgets.

Contribution

It presents a novel robust flow model with advantageous properties, including polynomial-time algorithms for key variants, and analyzes protection strategies with budget considerations.

Findings

Optimal robust flows can be computed in polynomial time for basic variants.

Protection with a budget can be efficiently solved when costs are chosen from scratch.

The problem becomes hard to approximate when improving existing protection infrastructure.

Abstract

Due to the importance of robustness in many real-world optimization problems, the field of robust optimization has gained a lot of attention over the past decade. We concentrate on maximum flow problems and introduce a novel robust optimization model which, compared to known models from the literature, features several advantageous properties: (i) We consider a general class of path-based flow problems which can be used to model a large variety of network routing problems (and other packing problems). (ii) We aim at solutions that are robust against targeted attacks by a potent adversary who may attack any flow path of his choice on any edge of the network. (iii) In contrast to previous robust maximum flow models, for which no efficient algorithms are known, optimal robust flows for the most important basic variants of our model can be found in polynomial time. We also consider generalizations where the flow player can spend a budget to protect the network against the interdictor. Here, we show that the problem can be solved efficiently when the interdiction costs are determined by the flow player from scratch. However, the problem becomes hard to approximate when the flow player has to improve an initial protection infrastructure.