The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
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
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
Navigable Small-World networks with few random bits
Theoretical Computer Science
Small worlds as navigable augmented networks: model, analysis, and validation
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Biased selection for building small-world networks
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
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We consider small world graphs as defined by Kleinberg (2000), i.e., graphs obtained from a d- dimensional mesh by adding links chosen at random according to the d-harmonic distribution. In these graphs, greedy routing performs in O (log2 n) expected number of steps. We introduce indirect-greedy routing. We show that giving O(log2 n) bits of topological awareness per node enables indirect-greedy routing to perform in O(log1+1/d n) expected number of steps in d-dimensional augmented meshes. We also show that, independently of the amount of topological awareness given to the nodes, indirect-greedy routing performs in Ω(log1+1/d n) expected number of steps. In particular, augmenting the topological awareness above this optimum of O(log2 n) bits would drastically decrease the performance of indirect-greedy routing.Our model demonstrates that the efficiency of indirect-greedy routing is sensitive to the "world's dimension," in the sense that high dimensional worlds enjoy faster greedy routing than low dimensional ones. This could not be observed in Kleinberg's routing. In addition to bringing new light to Milgram's experiment, our protocol presents several desirable properties. In particular, it is totally oblivious, i.e., there is no header modification along the path from the source to the target, and the routing decision depends only on the target, and on information stored locally at each node.