ScienceDirect - Computer Networks : Sampling large Internet topologies for simulation purposes

Computer Networks
Volume 51, Issue 15, 24 October 2007, Pages 4284-4302

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doi:10.1016/j.comnet.2007.06.004

Sampling large Internet topologies for simulation purposes

Vaishnavi Krishnamurthy ^a, Michalis Faloutsos ^a^,^,, Marek Chrobak ^a, Jun-Hong Cui ^b, Li Lao ^c and Allon G. Percus ^d

^aDepartment of Computer Science and Engineering, University of California Riverside, Riverside, CA 92521, United States ^bUniversity of Connecticut, Storrs, United States ^cU.C. Los Angeles, United States ^dLos Alamos National Labs, United States

Received 5 December 2006;

revised 23 May 2007;

accepted 5 June 2007.

Responsible Editor: M. Smirnow.

Available online 27 June 2007.

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Abstract

In this paper, we develop methods to “sample” a small realistic graph from a large Internet topology. Despite recent activity, modeling and generation of realistic graphs resembling the Internet is still not a resolved issue. All previous work has attempted to grow such graphs from scratch. We address the complementary problem of shrinking an existing topology. 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 an Internet graph by as much as 70% while maintaining its important properties. Second, we show that our reduced graphs compare favorably against construction-based generators. Finally, we successfully validate the effectiveness of our best methods in an actual performance evaluation study of multicast routing. Apart from its practical applications, the problem of graph sampling is of independent interest.

Keywords: Graph modeling; Graph sampling; Graph properties