Papillon: Greedy Routing in Rings

We construct the first n-node degree-d ring-based network with worst-case greedy routes of length Θ(log n / log d) hops.

[1]  de Ng Dick Bruijn A combinatorial problem , 1946 .

[2]  Sharon L. Milgram,et al.  The Small World Problem , 1967 .

[3]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[4]  Charles Delorme,et al.  Table of Large (Delta, D)-Graphs , 1992, Discret. Appl. Math..

[5]  F. Comellas,et al.  New large graphs with given degree and diameter , 1994, math/9411218.

[6]  H. T. Waterbolk Koninklijke Nederlandse Akademie van Wetenschappen , 1997 .

[7]  Jon M. Kleinberg,et al.  The small-world phenomenon: an algorithmic perspective , 2000, STOC '00.

[8]  Geoffrey Exoo,et al.  A family of graphs and the degree/diameter problem , 2001, J. Graph Theory.

[9]  Akademie van Wetenschappen,et al.  Koninklijke Nederlandse Akademie Van Wetenschappen , 2001 .

[10]  David R. Karger,et al.  Chord: A scalable peer-to-peer lookup service for internet applications , 2001, SIGCOMM '01.

[11]  Moni Naor,et al.  Viceroy: a scalable and dynamic emulation of the butterfly , 2002, PODC '02.

[12]  James Aspnes,et al.  Fault-tolerant routing in peer-to-peer systems , 2002, PODC '02.

[13]  Ramesh Govindan,et al.  Incrementally improving lookup latency in distributed hash table systems , 2003, SIGMETRICS '03.

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

[15]  Krishna P. Gummadi,et al.  The impact of DHT routing geometry on resilience and proximity , 2003, SIGCOMM '03.

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

[17]  Gurmeet Singh Manku,et al.  Symphony: Distributed Hashing in a Small World , 2003, USENIX Symposium on Internet Technologies and Systems.

[18]  Abhishek Kumar,et al.  Ulysses: a robust, low-diameter, low-latency peer-to-peer network , 2003, 11th IEEE International Conference on Network Protocols, 2003. Proceedings..

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

[20]  Rajeev Motwani,et al.  Dipsea: a modular distributed hash table , 2004 .

[21]  Abhishek Kumar,et al.  On the fundamental tradeoffs between routing table size and network diameter in peer-to-peer networks , 2004, IEEE J. Sel. Areas Commun..

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

[23]  Gurmeet Singh Manku,et al.  Optimal routing in Chord , 2004, SODA '04.