Finding events in temporal networks: Segmentation meets densest-subgraph discovery

TL;DR

This paper introduces a method for detecting significant events in temporal networks by identifying dense subgraphs over time intervals, using approximation algorithms to efficiently find high-quality solutions.

Contribution

It formulates the event discovery as an optimization problem and adapts approximation algorithms for efficient detection of dense subgraph events in temporal networks.

Findings

The proposed algorithm finds high-quality dense subgraph events.

Approximation methods enable scalable event detection.

Experimental results show effective event identification.

Abstract

In this paper we study the problem of discovering a timeline of events in a temporal network. We model events as dense subgraphs that occur within intervals of network activity. We formulate the event-discovery task as an optimization problem, where we search for a partition of the network timeline into k non-overlapping intervals, such that the intervals span subgraphs with maximum total density. The output is a sequence of dense subgraphs along with corresponding time intervals, capturing the most interesting events during the network lifetime. A naive solution to our optimization problem has polynomial but prohibitively high running time complexity. We adapt existing recent work on dynamic densest-subgraph discovery and approximate dynamic programming to design a fast approximation algorithm. Next, to ensure richer structure, we adjust the problem formulation to encourage coverage of a larger set of nodes. This problem is NP-hard even for static graphs. However, on static graphs a simple greedy algorithm leads to approximate solution due to submodularity. We extended this greedy approach for the case of temporal networks. However, the approximation guarantee does not hold. Nevertheless, according to the experiments, the algorithm finds good quality solutions.