The expansion and mixing time of skip graphs with applications

We prove that with high probability a skip graph contains a 4-regular expander as a subgraph, and estimate the quality of the expansion via simulations. As a consequence skip graphs contain a large connected component even after an adversarial deletion of nodes. We show how the expansion property could be used to sample a node in the skip graph in a highly efficient manner. We also show that the expansion property could be used to load balance the skip graph quickly. Finally it is shown that the skip graph could serve as an unstructured P2P system, thus it is a good candidate for a hybrid P2P system.

[1]  László Lovász,et al.  Random Walks on Graphs: A Survey , 1993 .

[2]  Moni Naor,et al.  Know thy neighbor's neighbor: the power of lookahead in randomized P2P networks , 2004, STOC '04.

[3]  Joel Friedman,et al.  A proof of Alon's second eigenvalue conjecture and related problems , 2004, ArXiv.

[4]  Maxwell Young,et al.  Choosing a Random Peer in Chord , 2007, Algorithmica.

[5]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[6]  Christos Gkantsidis,et al.  Random walks in peer-to-peer networks , 2004, IEEE INFOCOM 2004.

[7]  János Komlós,et al.  Deterministic simulation in LOGSPACE , 1987, STOC.

[8]  Antony I. T. Rowstron,et al.  Pastry: Scalable, Decentralized Object Location, and Routing for Large-Scale Peer-to-Peer Systems , 2001, Middleware.

[9]  Michael B. Jones,et al.  SkipNet: A Scalable Overlay Network with Practical Locality Properties , 2003, USENIX Symposium on Internet Technologies and Systems.

[10]  Jonathan Kirsch,et al.  Load balancing and locality in range-queriable data structures , 2004, PODC '04.

[11]  Noga Alon,et al.  Eigenvalues and expanders , 1986, Comb..

[12]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[13]  Ion Stoica,et al.  The Case for a Hybrid P2P Search Infrastructure , 2004, IPTPS.

[14]  Moni Naor,et al.  Novel architectures for P2P applications: the continuous-discrete approach , 2003, SPAA '03.

[15]  Gurmeet Singh Manku,et al.  Routing networks for distributed hash tables , 2003, PODC '03.

[16]  Robert Morris,et al.  Chord: A scalable peer-to-peer lookup service for internet applications , 2001, SIGCOMM 2001.

[17]  David R. Karger,et al.  Simple Efficient Load-Balancing Algorithms for Peer-to-Peer Systems , 2004, SPAA '04.

[18]  Noga Alon,et al.  lambda1, Isoperimetric inequalities for graphs, and superconcentrators , 1985, J. Comb. Theory, Ser. B.

[19]  Nicholas J. A. Harvey,et al.  Family trees: an ordered dictionary with optimal congestion, locality, degree, and search time , 2004, SODA '04.

[20]  Ben Y. Zhao,et al.  Tapestry: An Infrastructure for Fault-tolerant Wide-area Location and , 2001 .

[21]  Jared Saia,et al.  Choosing a random peer , 2004, PODC '04.

[22]  Ben Y. Zhao,et al.  An Infrastructure for Fault-tolerant Wide-area Location and Routing , 2001 .

[23]  Moni Naor,et al.  A Simple Fault Tolerant Distributed Hash Table , 2003, IPTPS.

[24]  James Aspnes,et al.  Skip graphs , 2003, SODA '03.