Sampling Regular Graphs and a Peer-to-Peer Network

d Abstract) Colin Cooper∗ , Martin Dyer† and Catherine Greenhill‡ We consider a simple Markov chain for d-regular graphs on n vertices, and show that the mixing time of this Markov chain is bounded above by a polynomial in n and d. A related Markov chain for d-regular graphs on a varying number of vertices is introduced, for even degree d. We use this to model a certain peer-to-peer network structure. We prove that the related chain has mixing time which is bounded by a polynomial in N, the expected number of vertices, under reasonable assumptions about the arrival and departure process.

• Type: Journal
• Year: 2007
• Where: CPC
• Authors: Colin Cooper, Martin E. Dyer, Catherine S. Greenhill
• Keywords: CPC 2007, D-regular Graphs, Markov Chain, Simple Markov Chain