The diameter of a cycle plus a random matching
SIAM Journal on Discrete Mathematics
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Chord: A scalable peer-to-peer lookup service for internet applications
Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications
The diameter of long-range percolation clusters on finite cycles
Random Structures & Algorithms
Fault-tolerant routing in peer-to-peer systems
Proceedings of the twenty-first annual symposium on Principles of distributed computing
The diameter of a long-range percolation graph
Random Structures & Algorithms
Efficient Routing in Networks with Long Range Contacts
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Know thy neighbor's neighbor: the power of lookahead in randomized P2P networks
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Eclecticism shrinks even small worlds
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Analyzing Kleinberg's (and other) small-world Models
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Symphony: distributed hashing in a small world
USITS'03 Proceedings of the 4th conference on USENIX Symposium on Internet Technologies and Systems - Volume 4
A doubling dimension threshold θ(loglogn) for augmented graph navigability
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Navigable Small-World networks with few random bits
Theoretical Computer Science
A Lower Bound for Network Navigability
SIAM Journal on Discrete Mathematics
Optimal path search in small worlds: dimension matters
Proceedings of the forty-third annual ACM symposium on Theory of computing
Using multiagent self-organization techniques for seeking information in virtual social communities
Web Intelligence and Agent Systems
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In order to explain the ability of individuals to find short paths to route messages to an unknown destination, based only on their own local view of a social network (the small world phenomenon), Kleinberg [The small-world phenomenon: an algorithmic perspective, Proc. 32nd ACM Symp. on Theory of Computing, 2000, pp. 163-170] proposed a network model based on a d-dimensional lattice of size n augmented with k long-range directed links per node. Individuals behavior is modeled by a greedy algorithm that, given a source and destination, forwards a message to the neighbor of the current holder, which is the closest to the destination. This algorithm computes paths of expected length Θ(log2 n/k) between any pair of nodes. Other topologies have been proposed later on to improve greedy algorithm performance. But, Aspnes et al. [Fault-tolerant routing in peer-to-peer systems, in: Proc. of ACM 3st Symp. on Princ. of Distr. Comp. (PODC 2002), Vol. 31, 2002, pp. 223-232] shows that for a wide class of long-range link distributions, the expected length of the path computed by this algorithm is always Ω(log2 n/(k2 log log n)).We design and analyze a new decentralized routing algorithm, in which nodes consult their neighbors near by, before deciding to whom forward the message. Our algorithm uses similar amount of computational resources as Kleinberg's greedy algorithm: it is easy to implement, visits O(log2 n/log2 (1 +k)) nodes on expectation and requires only Θ(log2 n/log(1 +k)) bits of memory--note that [G.S. Manku, M. Naor, U. Wieder, Know thy neighbor's neighbor: the power of lookahead in randomized P2P networks, in: Proc. of 36th ACM STOC 2004, 2004, to appear], shows that any decentralized algorithm visits at least Ω(log2 n/k) on expectation. Our algorithm computes however a path of expected length O(log n (log log n)2/log2 (1 + k)) between any pair of nodes. Our algorithm might fit better some human social behaviors (such as web browsing) and may also have successful applications to peer-to-peer networks where the length of the path along which the files are downloaded, is a critical parameter of the network performance.