Real‐time monitoring of undirected networks: Articulation points, bridges, and connected and biconnected components

Abstract

In this article, we present the first algorithm in the streaming model to characterize completely the biconnectivity properties of undirected networks: articulation points, bridges, and connected and biconnected components. The motivation of our work was the development of a real-time algorithm to monitor the connectivity of the autonomous systems (AS) network, but the solution provided is general enough to be applied to any network. The network structure is represented by a graph, and the algorithm is analyzed in the datastream framework. Here, as in the on-line model, the input graph is revealed one item (i.e., graph edge) after the other, in an on-line fashion; but, if compared to traditional on-line computation, there are stricter requirements for both memory occupation and per item processing time. Our algorithm works by properly updating a forest over the graph nodes. All the graph (bi)connectivity properties are stored in this forest. We prove the correctness of the algorithm, together with its space (O(nlog n), with n being the number of nodes in the graph) and time bounds. We also present the results of a brief experimental evaluation against real-world graphs, including many samples of the AS network, ranging from medium to massive size. These preliminary experimental results confirm the effectiveness of our approach. © 2012 Wiley Periodicals, Inc. NETWORKS, Vol. 2012 Copyright © 2012 Wiley Periodicals, Inc

Real-time anomalies detection and analysis of network structure, with application to the Autonomous System network

“…As previously mentioned, the algorithm is fully detailed in [4], where is provided both a theoretical analysis and an experimental evaluation. On the theoretical side, the algorithm processes a streaming graph, with n vertices and m edges, in O(n log n + mα(m, n)); the space usage is O(n log n), that is tight, in the sense that, for particular graph instances, it is the space needed to store part of the solution (the list of all the bridges); on the experimental evaluation side, the implementation, on an off-the-shelf laptop (with a 2-Ghz CPU running GNU/Linux), is able to process more than one million edges per second.…”

“…In this section we provide a high level view of the algorithm, that is fully detailed in [4]. The main idea behind the algorithm, called "At First Look" (AFL), is to keep in main memory a particular forest structure that provides all the (bi)connectivity information of the graph seen so far from the input stream; an example of this structure, called navigational sketch (NS), is depicted in Figure 2.…”

“…The algorithm, fully described in [4], has been experimentally validated against real-world graphs up to hundreds of millions nodes and billions edges, and it is able to process about one million edges per second on an off-the-shelf laptop. Therefore, the tool can be easily adapted to monitor the traffic flows in medium and large scale networks.…”

Spectral partitioning for node criticality

“…This effect can vary from having a small decrease in the QoS of a portion of the network upto the complete breakdown of the network [1]. In March 2011, a Georgian woman who was scavenging for copper to sell as scrap, cut off the web access to almost the whole of Armenia [2]. She damaged the main fiber optic that was connecting 90% of Armenia thus, depriving 3.2 million people from the access to the internet for five hours.…”

“…Among various nodes that exist in the network, the nodes that have the highest influence on the performance of the network upon their removal are referred to as the Critical Nodes (CNs) of a network [2]. The identification of these CNs beforehand leads to an appreciation of the vulnerability of a network and in some cases aid in formulating a suitable solution which can help avoid, the degradation in performance or the network partitioning that will result from node failure.…”