Randomized algorithms
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
Efficient Routing in Networks with Long Range Contacts
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Proximate planar point location
Proceedings of the nineteenth annual symposium on Computational geometry
Geographic routing for wireless networks
Geographic routing for wireless networks
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry — CCCG02
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
Analyzing and characterizing small-world graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Could any graph be turned into a small-world?
Theoretical Computer Science - Complex networks
Geographic routing made practical
NSDI'05 Proceedings of the 2nd conference on Symposium on Networked Systems Design & Implementation - Volume 2
Greedy routing in tree-decomposed graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Recovering the Long-Range Links in Augmented Graphs
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
The effect of power-law degrees on the navigability of small worlds: [extended abstract]
Proceedings of the 28th ACM symposium on Principles of distributed computing
Recovering the long-range links in augmented graphs
Theoretical Computer Science
Deterministic decentralized search in random graphs
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Small worlds as navigable augmented networks: model, analysis, and validation
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Depth of field and cautious-greedy routing in social networks
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
A sociability-based routing scheme for delay-tolerant networks
EURASIP Journal on Wireless Communications and Networking - Special issue on opportunistic and delay tolerant networks
Indexing Network Structure with Shortest-Path Trees
ACM Transactions on Knowledge Discovery from Data (TKDD)
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Social networks are navigable small worlds, in which two arbitrary people are likely connected by a short path of intermediate friends that can be found by a "decentralized" routing algorithm using only local information. We develop a model of social networks based on an arbitrary metric space of points, with population density varying across the points. We consider rank-based friendships, where the probability that person u befriends person v is inversely proportional to the number of people who are closer to u than v is. Our main result is that greedy routing can find a short path (of expected polylogarithmic length) from an arbitrary source to a randomly chosen target, independent of the population densities, as long as the doubling dimension of the metric space of locations is low. We also show that greedy routing finds short paths with good probability in tree-based metrics with varying population distributions.