Incremental Algorithms for Sampling Dynamic Graphs

Abstract

Among the many reasons that justify the need for efficient and effective graph sampling algorithms is the ability to replace a graph too large to be processed by a tractable yet representative subgraph. For instance, some approximation algorithms start by looking for a solution on a sample subgraph and then extrapolate it. The sample graph should be of manageable size. The sample graph should preserve properties of interest. There exist several efficient and effective algorithms for the sampling of graphs. However, the graphs encountered in modern applications are dynamic: edges and vertices are added or removed. Existing graph sampling algorithms are not incremental. They were designed for static graphs. If the original graph changes, the sample must be entirely recomputed. Is it possible to design an algorithm that reuses whole or part of the already computed sample?

We present two incremental graph sampling algorithms preserving selected properties. The rationale of the algorithms is to replace a fraction of vertices in the former sample with newly updated vertices. We analytically and empirically evaluate the performance of the proposed algorithms. We compare the performance of the proposed algorithms with that of baseline algorithms. The experimental results on both synthetic and real graphs show that our proposed algorithms realize a compromise between effectiveness and efficiency, and, therefore provide practical solutions to the problem of incrementally sampling the large dynamic graphs.