Work

A bilevel critical node detection problem

Year: 2025

Type: article

Abstract: In this study, we formulate a bilevel critical node detection problem for a given threat level and a budget. A leader has a budget to immunize a subset of nodes. An attacker, with the knowledge of the leader’s choice, will remove any set of non-immunized nodes within their budget, which is the threat level. The leader seeks to maximise the pairwise connectivity of the nodes for the worst case removal strategy of the attacker. We solve this problem using a high point relaxation within a branch-and-bound framework. We introduce some valid inequalities to strengthen the formulation and introduce a branching strategy to deal with the bilevel infeasibility. We test this procedure on two graph families with varying number of nodes, edge densities and budgets and share our computational experience.

Source: Optimization Letters

DOI: 10.1007/s11590-025-02258-6

Authors: Ashwin Arulselvan, Altannar Chinchuluun, Panos Pardalos

Institutions: University of Strathclyde, National University of Mongolia, University of Florida

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

OpenAlex ID: W7101401294