The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of 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
Analyzing and characterizing small-world graphs
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Universal augmentation schemes for network navigability: overcoming the √n-barrier
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ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
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ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
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Recovering the Long-Range Links in Augmented Graphs
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Universal augmentation schemes for network navigability
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Proceedings of the 9th ACM/IEEE-CS joint conference on Digital libraries
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
Navigable Small-World networks with few random bits
Theoretical Computer Science
Do neighbor-avoiding walkers walk as if in a small-world network?
INFOCOM'09 Proceedings of the 28th IEEE international conference on Computer Communications Workshops
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
Non-searchability of random power-law graphs
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
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
Could any graph be turned into a small-world?
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Category-based routing in social networks: Membership dimension and the small-world phenomenon
Theoretical Computer Science
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In addition to statistical graph properties (diameter, degree, clustering, etc.), Kleinberg [The small-world phenomenon: an algorithmic perspective, in: Proc. 32nd ACM Symp. on Theory of Computing (STOC), 2000, pp. 163-170] showed that a small-world can also be seen as a graph in which the routing task can be efficiently and easily done in spite of a lack of global knowledge. More precisely, in a lattice network augmented by extra random edges (but not chosen uniformly), a short path of polylogarithmic expected length can be found using a greedy algorithm with a local knowledge of the nodes. We call such a graph a navigable small-world since short paths exist and can be followed with partial knowledge of the network. In this paper, we show that a wide class of graphs can be augmented into navigable small-worlds.