Topology-Based Spectral Sparsification

Graph sampling is often used to reduce a large graph, with challenges to ensure the sample is representative of the original graph. Spectral sparsification is a related concept that creates a sparsified version of graphs that preserves the spectrum of the original graph. We present TSS, a sampling method combining spectral sparsification with topology-based decomposition of graphs. TSS aims to improve the runtime efficiency of spectral sparsification-based sampling through a Divide-and-Conquer approach using topology-based decomposition and combine it with the superior sampling quality spectral sparsification-based sampling offers over stochastic sampling. We also present DTSS, the distributed version of TSS, aimed for further runtime gains over sequential TSS. Experiments verify that TSS produces samples of the same quality as spectral sparsification-based sampling while attaining significant runtime improvements of up to 60% on real world datasets. DTSS on 5 servers runs up to another 80% faster compared to TSS.