Real-Time Monitoring of Undirected Networks: Articulation Points, Bridges, and Connected and Biconnected Components

TL;DR

This paper introduces the first streaming algorithm for real-time detection of articulation points, bridges, and connectivity components in undirected networks, suitable for monitoring large-scale dynamic systems like the AS network.

Contribution

The paper presents a novel streaming algorithm that efficiently characterizes biconnectivity properties in undirected graphs with strict memory and processing constraints.

Findings

Algorithm correctly identifies connectivity properties.

Space complexity is $O(n \,\log n)$.

Experimental results confirm effectiveness on real-world graphs.

Abstract

In this paper 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 \emph{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 ($O(n\,\log n)$, 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.