Spectral Algorithms for Temporal Graph Cuts
Arlei Silva, Ambuj Singh, Ananthram Swami

TL;DR
This paper introduces spectral algorithms for identifying meaningful cuts in dynamic, temporal graphs, extending traditional static graph cut concepts to capture temporal smoothness and dynamic community structures.
Contribution
It presents novel formulations and algorithms for temporal graph cuts using spectral methods, multiplex graphs, and low-rank approximations, addressing the dynamic nature of modern graphs.
Findings
Algorithms are accurate and scalable.
Effective in discovering dynamic communities.
Applicable to dynamic graph signal analysis.
Abstract
The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of graph cuts include community detection and computer vision. However, cut problems were originally proposed for static graphs, an assumption that does not hold in many modern applications where graphs are highly dynamic. In this paper, we introduce the sparsest and normalized cut problems in temporal graphs, which generalize their standard definitions by enforcing the smoothness of cuts over time. We propose novel formulations and algorithms for computing temporal cuts using spectral graph theory, multiplex graphs, divide-and-conquer and low-rank matrix approximation. Furthermore, we extend our formulation to dynamic graph signals, where cuts also…
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Taxonomy
TopicsOpportunistic and Delay-Tolerant Networks · Complex Network Analysis Techniques · Caching and Content Delivery
