Discounted Cuts: A Stackelberg Approach to Network Disruption

TL;DR

This paper introduces a new model called discounted cuts to analyze network disruption games, providing polynomial algorithms for certain graph classes and revealing complex computational properties.

Contribution

It develops a unified framework for discounted cut problems, generalizes the Most Vital Links problem, and proves polynomial solvability for bounded-genus graphs.

Findings

Polynomial-time algorithms for discounted cut problems on bounded-genus graphs

NP-completeness of many variants on general graphs

New insights into attacker-defender interactions in network disruption

Abstract

We study a Stackelberg variant of the classical Most Vital Links problem, modeled as a one-round adversarial game between an attacker and a defender. The attacker strategically removes up to $k$ edges from a flow network to maximally disrupt flow between a source $s$ and a sink $t$, after which the defender optimally reroutes the remaining flow. To capture this attacker--defender interaction, we introduce a new mathematical model of discounted cuts, in which the cost of a cut is evaluated by excluding its $k$ most expensive edges. This model generalizes the Most Vital Links problem and uncovers novel algorithmic and complexity-theoretic properties. We develop a unified algorithmic framework for analyzing various forms of discounted cut problems, including minimizing or maximizing the cost of a cut under discount mechanisms that exclude either the $k$ most expensive or the $k$ cheapest edges. While most variants are NP-complete on general graphs, our main result establishes polynomial-time solvability for all discounted cut problems in our framework when the input is restricted to bounded-genus graphs, a relevant class that includes many real-world networks such as transportation and infrastructure networks. With this work, we aim to open collaborative bridges between artificial intelligence, algorithmic game theory, and operations research.