A preliminary analysis of the Distance Based Critical Node Problem

doi:10.1016/j.endm.2016.10.007

Electronic Notes in Discrete Mathematics

Volume 55, November 2016, Pages 25-28

https://doi.org/10.1016/j.endm.2016.10.007 Get rights and content

Abstract

We discuss how to develop efficient heuristics for the distance based critical node problem, that is the problem of deleting a subset of nodes from a graph G in such a way that the distance between each pair of nodes is as large as possible.

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There are more references available in the full text version of this article.

Cited by (6)

A fast tri-individual memetic search approach for the distance-based critical node problem
2023, European Journal of Operational Research
Citation Excerpt :
Besides general graphs, Aringhieri, Grosso, Hosteins, & Scatamacchia (2019) presented dynamic programming algorithms for DCNP over special graph classes such as paths, trees, and series-parallel graphs. To solve DCNP approximately, Aringhieri et al. (2016c) performed a preliminary analysis and provided some suggestions on designing heuristic algorithms. Alozie et al. (2022) presented a centrality-based heuristic (CBH) algorithm for DCNP, which combined a backbone-based crossover procedure to generate an offspring solution and a centrality-based neighborhood search to improve it.
The distance-based critical node problem involves identifying a subset of nodes in a graph such that the removal of these nodes leads to a residual graph with the minimum distance-based connectivity. Due to its NP-hard nature, solving this problem using exact algorithms has proved to be highly challenging. Moreover, existing heuristic algorithms are typically time-consuming. In this work, we introduce a fast tri-individual memetic search approach to solve the problem. The proposed approach maintains a small population of only three individuals during the whole search. At each generation, it sequentially executes an inherit-repair recombination operator to generate a promising offspring solution, a fast betweenness centrality-based late-acceptance search to find high-quality local optima, and a simple population updating strategy to maintain a healthy population. Extensive experiments on both real-world and synthetic benchmarks show our method significantly outperforms state-of-the-art algorithms. In particular, it can steadily find the known optimal solutions for all 22 real-world instances with known optima in only one minute, and new upper bounds on the remaining 22 large real-world instances. For 54 synthetic instances, it finds new upper bounds on 36 instances, and matches the previous best-known upper bounds on 15 other instances in ten minutes. Finally, we investigate the usefulness of each key algorithmic ingredient.
Efficient Benders decomposition for distance-based critical node detection problem
2020, Omega (United Kingdom)
Citation Excerpt :
They formulated the problem as an MILP and proposed an exact algorithm to solve it. Later, Aringhieri et al. [25] considered the development of efficient heuristics to solve DCNDPs. Gillen, et al. [26] addressed DCNDP assuming that there exists some level of misinformation about the network, and compared the performance of the solutions obtained by exact algorithms and the ones provided by heuristics.
This paper addresses the critical node detection problem which seeks a subset of nodes for removal in order to maximize the disconnectivity of the residual graph with respect to a specific distance-based measure, namely the Wiener index. Such a measure is defined based on the all-pair shortest path distances in the residual graph so that the longer the total length of shortest paths, the greater the value of the disconnectivity measure. In the literature, a mixed integer linear programming model and an exact iterative-based method have been presented for this problem; however, both approaches become very time-consuming on graphs having large diameter and non-unit edge lengths. To overcome this shortcoming, in this paper, we present a new formulation for the problem and solve it by Benders decomposition algorithm. We improve the performance of Benders algorithm by several techniques (including analytical calculation of dual variables, generation of good-quality initial optimality cuts, considering master's optimality cuts as lazy constraints, etc.) to reduce the total running time. The extensive computational experiments on instances, taken from the literature or generated randomly, confirm the effectiveness of the new approaches.
Polynomial and pseudo-polynomial time algorithms for different classes of the Distance Critical Node Problem
2019, Discrete Applied Mathematics
We study the Distance Critical Node Problem, a generalisation of the Critical Node Problem where the distances between node pairs impact on the objective function. We establish complexity results for the problem according to specific distance functions and provide polynomial and pseudo-polynomial algorithms for special graph classes such as paths, trees and series–parallel graphs. We also provide additional insights about special cases of the Critical Node Problem variants already tackled in the literature.
The Critical Node Detection Problem in networks: A survey
2018, Computer Science Review
Citation Excerpt :
We can note that few studies have been conducted especially in the case of general graphs for almost all variants. Examples of the few works dealing with this are [112,113]. It is also interesting to consider different variants on directed graphs, as many real-world networks are modeled by digraphs, for example: web, scheduling networks, research citation networks, transport networks, etc.
In networks, not all nodes have the same importance, and some are more important than others. The issue of finding the most important nodes in networks has been addressed extensively, particularly for nodes whose importance is related to network connectivity. These nodes are usually known as Critical Nodes. The Critical Node Detection Problem (CNDP) is the optimization problem that consists in finding the set of nodes, the deletion of which maximally degrades network connectivity according to some predefined connectivity metrics. Recently, this problem has attracted much attention, and depending on the predefined metric, different variants have been developed. In this survey, we review, classify and discuss several recent advances and results obtained for each variant, including theoretical complexity, exact solving algorithms, approximation schemes and heuristic approaches. We also prove new complexity results and induce some solving algorithms through relationships established between different variants.
A heuristic approach for the distance-based critical node detection problem in complex networks
2022, Journal of the Operational Research Society
A polynomial-time algorithm for finding critical nodes in bipartite permutation graphs
2019, Optimization Letters

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A preliminary analysis of the Distance Based Critical Node Problem

Abstract

Electronic Notes in Discrete Mathematics

Computers & Operations Research

Hybrid Constructive Heuristics for the Critical Node Problem

Annals of Operations Research

Local Search Metaheuristics for the Critical Node Problem

Networks