Distributed Identification of the Most Critical Node for Average Consensus

Abstract

In communication networks, cyber attacks, such as resource depleting attacks, can cause failure of nodes and can damage or significantly slow down the convergence of the average consensus algorithm. In particular, if the network topology information is learned, an intelligent adversary can attack the most critical node in the sense that deactivating it causes the largest destruction, among all the network nodes, to the convergence speed of the average consensus algorithm. Although a centralized method can undoubtedly identify such a critical node, it requires global information and is computationally intensive and, hence, is not scalable. In this paper, we aim to identify the most critical node in a distributed manner. The network algebraic connectivity is used to assess the destruction caused by node removal and further the importance of a node. We propose three low-complexity algorithms to estimate the descent of the algebraic connectivity due to node removal and theoretically analyze the corresponding estimation errors. Based on these estimation algorithms, distributed power iteration, and maximum-consensus, we propose a fully distributed algorithm for the nodes to iteratively find the most critical one. Extensive simulation results demonstrate the effectiveness of the proposed methods.Index Terms-Consensus, critical node identification, algebraic connectivity, Fiedler vector, distributed algorithm. 1053-587X

The impact of elimination of the most critical node on Wireless Sensor Network lifetime

“…In addition to malicious acts, some topologies may have environmental and natural risks such as falling trees, earthquakes, landslides which can render some sensor nodes permanently inoperable. Since, even a single node has a crucial factor in the integrity of the WSN, the most critical node could be detected before performing any of these attack types [14]- [16]. Although, defense strategies for node specific attacks were developed (e.g., [17]), they still require to sacrifice some sensor nodes.…”

Optimization based spectral partitioning for node criticality assessment

“…On the other hand, examples of topology based schemes include: the eigenvector centrality metric [23], which uses the largest eigenvector of the adjacency matrix, the Hybrid Interactive Linear Programming Rounding (HILPR) algorithm [13], which analyses the effect that a node has on the pair-wise connectivity of a network upon its removal, the GREEDY Critical Node Detection Problem approach (GREEDY-CNDP) [24] and the β − disruptor approach proposed in [25], both of which propose an efficient algorithm to minimize pairwise connectivity upon removal of k nodes, the degree centrality metric [16] [17] which uses the degree of each node, the dynamic programming approach in [26] which proposes polynomial time algorithms to find maximally disconnected graphs with maximum number of maximal connected components and minimum largest component sizes and algebraic connectivity based approaches [27] [28] [29] [30] [31] [32] which attempt to minimize the algebraic connectivity upon node removal.…”

“…In addition, when multiple critical nodes need to be found the approach becomes computationally expensive with the number of subgraphs that need to be considered increasing combinatorially with the network size. For this reason, a number of suboptimal solutions have been proposed in literature [30][31] [28] [29]. These suboptimal solutions utilize the elements of the Fiedler vector which is the eigenvector associated with the second smallest eigenvalue of the Laplacian of the network.…”

Combined Banzhaf & Diversity Index (CBDI) for critical node detection

“…The node criticality problem has also been viewed as an algebraic connectivity minimization problem, where the most critical nodes are the ones which minimize the algebraic connectivity of the network [11]. Since the solution of the optimization problem becomes computationally expensive to find as the size of the network increases, a number of suboptimal solutions have been proposed in literature [12][13] [14]. Another set of approaches that exist in literature are based on the ability of nodes to fragment the network when removed.…”