On New Approaches of Assessing Network Vulnerability: Hardness and Approximation

Abstract

Abstract-Society relies heavily on its networked physical infrastructure and information systems. Accurately assessing the vulnerability of these systems against disruptive events is vital for planning and risk management. Existing approaches to vulnerability assessments of large-scale systems mainly focus on investigating inhomogeneous properties of the underlying graph elements. These measures and the associated heuristic solutions are limited in evaluating the vulnerability of large-scale network topologies. Furthermore, these approaches often fail to provide performance guarantees of the proposed solutions. In this paper, we propose a vulnerability measure, pairwise connectivity, and use it to formulate network vulnerability assessment as a graph-theoretical optimization problem, referred to as β-disruptor. The objective is to identify the minimum set of critical network elements, namely nodes and edges, whose removal results in a specific degradation of the network global pairwise connectivity. We prove the NP-Completeness and inapproximability of this problem, and propose an O(log n log log n) pseudoapproximation algorithm to computing the set of critical nodes and an O(log 1.5 n) pseudo-approximation algorithm for computing the set of critical edges. The results of an extensive simulation-based experiment show the feasibility of our proposed vulnerability assessment framework and the efficiency of the proposed approximation algorithms in comparison with other approaches.

An efficient spectral bound for link vulnerability assessment in large-scale networks

“…The number of connected node pairs in the network, (a.k.a pairwise connectivity), lends itself as an effective measure to account for the effect of the attacks [1], [2], [3], [4], [5], [6], [7].…”

“…Vulnerability assessment has been recently formulated as an connectivity optimization problem called β-edge disruptor, which finds a minimum cost links whose removal causes a significant level (β) of network pairwise degradation [6]. The β-edge disruptor reflects the common sense that when breaking the network by removing links, the more links required to be removed, the less vulnerable the network is.…”

“…Unfortunately, the β-edge disruptor problem is NP-hard [6] i.e. there is no efficient algorithm to solve the problem, unless P=NP.…”

“…there is no efficient algorithm to solve the problem, unless P=NP. A pseudo-approximation algorithm and mathematical approaches for the β-edge disruptor problems are introduced in [6] and [5], respectively. Although those methods can provide performance guarantees, they are only applicable for small and medium networks of few thousand nodes.…”

“…Related work. Many existing works on network vulnerability assessment mainly focus on the local centrality measurements to differentiate between critical links and nodes and the others, see [9], [6]. Other global graph measures have also been proposed to assess network vulnerability.…”