A heuristic approach for the distance-based critical node detection problem in complex networks

Kerem Akartunalı,Eduardo L. Pasiliao,Ashwin Arulselvan,Glory Uche Alozie

doi:10.1080/01605682.2021.1913078

Kerem Akartunalı, Eduardo L. Pasiliao + Show 2 more

Open Access

https://doi.org/10.1080/01605682.2021.1913078

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Abstract

The distance-based critical node problem involves identifying a subset of nodes in a network whose removal minimises a pre-defined distance-based connectivity measure. Having the classical critical node problem as a special case, the distance-based critical node problem is computationally challenging. In this article, we study the distance-based critical node problem from a heuristic algorithm perspective. We consider the distance-based connectivity objective whose goal is to minimise the number of node pairs connected by a path of length at most k, subject to budgetary constraints. We propose a centrality based heuristic which combines a backbone-based crossover procedure to generate good offspring solutions and a centrality-based neighbourhood search to improve the solution. Extensive computational experiments on real-world and synthetic graphs show the effectiveness of the developed heuristic in generating good solutions when compared to exact solution. Our empirical results also provide useful insights for future algorithm development.

Highlights

Assessment of system vulnerability to adversarial attacks has become an important concern to organisations especially in the wake of security threats around the world
To the best of our knowledge, the memetic algorithm proposed by Zhou et al (2018) is the current state-of-the-art heuristic algorithm for the traditional critical node problem based on computational experiments on 26 real-world and 16 synthetic benchmark instances
4.3.3 Benchmark instances We extend our computational experiment to the set of benchmark synthetic graphs which have been used as test instances for most heuristic algorithms developed for the classical critical node detection problem

Summary

Introduction

Assessment of system vulnerability to adversarial attacks has become an important concern to organisations especially in the wake of security threats around the world. Unlike fragmentation-based CNP, the DCNP does consider whether a pair of nodes is connected and seeks to measure the extent of connectivity between them This is important in communication and social network contexts, where disconnection cannot be limited to absence of a path between node pairs. The authors observed that certain structural deviations from the input network are left undetected by traditional CNP metrics Traditional exact algorithms such as branch-andbound and branch-and-cut have been employed to solve critical node detection problem To the best of our knowledge, the memetic algorithm proposed by Zhou et al (2018) is the current state-of-the-art heuristic algorithm for the traditional critical node problem based on computational experiments on 26 real-world and 16 synthetic benchmark instances. We demonstrate the efficiency of our proposed algorithm in comparison to the current state-of-the-art algorithm on both real-world and synthetic graphs

Contributions

Organisation

Problem description

Heuristic for distance-based critical node problem

Representation and evaluation of feasible solution

General framework of heuristic

Initial solution generation

Backbone-based crossover

Centrality-based neighbourhood search

Test instances

Experimental settings

Performance of the heuristic algorithm