Reducing Large Internet Topologies for Faster Simulations

Abstract

Abstract. In this paper, we develop methods to "sample" a small realistic graph from a large real network. Despite recent activity, the modeling and generation of realistic graphs is still not a resolved issue. All previous work has attempted to grow a graph from scratch. We address the complementary problem of shrinking a graph. In more detail, this work has three parts. First, we propose a number of reduction methods that can be categorized into three classes: (a) deletion methods, (b) contraction methods, and (c) exploration methods. We prove that some of them maintain key properties of the initial graph. We implement our methods and show that we can effectively reduce the nodes of a graph by as much as 70% while maintaining its important properties. In addition, we show that our reduced graphs compare favourably against construction-based generators. Apart from its use in simulations, the problem of graph sampling is of independent interest.

Sampling large Internet topologies for simulation purposes

“…Our tool will be publicly available for research purposes. Finally, note that this work is a more extended version of our earlier work [28]. This version has: (a) the complete proof in Section 4, which was omitted in the earlier version, (b) a more extensive set of experiments and plots, namely 12 more plots, and (c) a more comprehensive list of previous and related efforts.…”

“…Despite some algorithmic similarities, these methods cannot be applied directly to our graph reduction problem. More recently, and after the conference version of our work [28], a datamining study [29] examines sampling of large graphs of multiple different origins.…”

Scalable graph exploration and visualization: Sensemaking challenges and opportunities

“…Filtering [1], [2], [3] Sampling [4], [5], [6] Partitioning [7], [8], [9], [10] Clustering [11], [12], [13], [3], [14], [15] Local View Free Discovery Exploration [16], [17], [14], [18], [3], [15], [19], [20], [21] Network Motifs [22], [23], [24], [25], [26] Targeted Discovery Pattern Matching [27], [28], [29], [30], [31] Navigation [32], [33], [34], [35], [36], [19], [37] Fig. 1.…”

“…The stochastic approaches use random sampling techniques to capture a smaller representative graph. A comparison of these approaches and others can be found in [4] and [6].…”

Metropolis Algorithms for Representative Subgraph Sampling

“…Thus the original graph is shrunken to a sample. The number of nodes can be reduced by as much as 70% while preserving important graph properties [8]. Furthermore sampling schemes were developed and investigated for visualization [15].…”