Full Record

Author | Edalatmanesh, Mahmood |

Title | Heuristics for the Critical Node Detection Problem in Large Complex Networks |

URL | http://hdl.handle.net/10464/4984 |

Publication Date | 2013 |

Date Accessioned | 2013-09-12 13:00:41 |

Discipline/Department | Department of Computer Science |

University/Publisher | Brock University |

Abstract | Complex networks have recently attracted a significant amount of research attention due to their ability to model real world phenomena. One important problem often encountered is to limit diffusive processes spread over the network, for example mitigating pandemic disease or computer virus spread. A number of problem formulations have been proposed that aim to solve such problems based on desired network characteristics, such as maintaining the largest network component after node removal. The recently formulated critical node detection problem aims to remove a small subset of vertices from the network such that the residual network has minimum pairwise connectivity. Unfortunately, the problem is NP-hard and also the number of constraints is cubic in number of vertices, making very large scale problems impossible to solve with traditional mathematical programming techniques. Even many approximation algorithm strategies such as dynamic programming, evolutionary algorithms, etc. all are unusable for networks that contain thousands to millions of vertices. A computationally efficient and simple approach is required in such circumstances, but none currently exist. In this thesis, such an algorithm is proposed. The methodology is based on a depth-first search traversal of the network, and a specially designed ranking function that considers information local to each vertex. Due to the variety of network structures, a number of characteristics must be taken into consideration and combined into a single rank that measures the utility of removing each vertex. Since removing a vertex in sequential fashion impacts the network structure, an efficient post-processing algorithm is also proposed to quickly re-rank vertices. Experiments on a range of common complex network models with varying number of vertices are considered, in addition to real world networks. The proposed algorithm, DFSH, is shown to be highly competitive and often outperforms existing strategies such as Google PageRank for minimizing pairwise connectivity. |

Subjects/Keywords | Complex networks, Heuristic, Critical node detection, Network model |

Language | en |

Country of Publication | ca |

Record ID | handle:10464/4984 |

Repository | brock |

Date Retrieved | 2020-04-30 |

Date Indexed | 2020-05-01 |

Issued Date | 2013-09-12 00:00:00 |

Sample Search Hits | Sample Images

…Gene Disease, and
Bipartite Disease networks when k = 50% . . . . . . . . . . . . . . . . . . . . . 129
Chapter 1
Introduction
The main objective of this thesis is to develop efficient heuristics for the *critical* *node*
detection problem (CNDP…

…size needs to be taken into consideration.
Removing nodes randomly from a graph and studying effects of such removals on
connectivity of graph has been studied extensively for regular graphs [16]. However,
many *critical* *node* detection problems…

…x5B;23, 24], and the diameter [2]).
Although variants of the *critical* *node* detection problem have been studied before,
this thesis focuses on a recently proposed CNDP [4]. Borgatti [17] proposed a new definition…

…of *critical* *node* based on pairwise connectivity after removing a certain number
of nodes from a network. This problem was later formally defined by Aruleslvan et al.
[4] and it was called the *critical* *node* detection problem (CNDP)…

…*critical* *node*" definition are given.
2.1 Graphs
A graph G = (V, E ) is a pair (V ,E ) such that V is the set of vertices and E is the set of
edges, where each edge is an unordered pair of vertices from set V . The number of…

…BACKGROUND
9
2.2 The *Critical* *Node* Detection Problem
The *critical* *node* detection problem was formally defined by Aruleslvan et al. [4] in
2009. This definition was derived from the work done by Borgatti who studied *critical*
*node* detection based on…

…x28;2.4)
So the *critical* *node* detection problem can be defined as:
Mi ni mi ze
ui j
(2.5)
i , j ∈V
sub j ect t o
u i j + v i + v j ≥ 1, ∀(i , j ) ∈ E ,
(2.6)
u i j + u j w − u kw ≤ 1, ∀i , j , w ∈ V,
(2.7…

…was aimed to find the most suitable properties that help to indicate the *critical* nodes of a graph in the context of the CNDP.
2.4.1 Cut vertices, Bridges, and Biconnected-components
A *node* v of a graph G is a cut vertex if removing *node* v and its…