The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Using the small-world model to improve freenet performance
ACM SIGCOMM Computer Communication Review
Fault-tolerant routing in peer-to-peer systems
Proceedings of the twenty-first annual symposium on Principles of distributed computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Efficient Routing in Networks with Long Range Contacts
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
ECDL '99 Proceedings of the Third European Conference on Research and Advanced Technology for Digital Libraries
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
IJCAI'99 Proceedings of the 16th international joint conference on Artificial intelligence - Volume 2
Greedy routing in tree-decomposed graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Universal augmentation schemes for network navigability: overcoming the √n-barrier
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
A doubling dimension threshold θ(loglogn) for augmented graph navigability
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
On the complexity of greedy routing in ring-based peer-to-peer networks
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Polylogarithmic network navigability using compact metrics with small stretch
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Recovering the Long-Range Links in Augmented Graphs
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Tight lower bounds for greedy routing in uniform small world rings
Proceedings of the forty-first annual ACM symposium on Theory of computing
Brief announcement: tight lower bounds for greedy routing in uniform small world rings
Proceedings of the 28th ACM symposium on Principles of distributed computing
Recovering the long-range links in augmented graphs
Theoretical Computer Science
Small worlds as navigable augmented networks: model, analysis, and validation
ESA'07 Proceedings of the 15th annual European conference on Algorithms
A Lower Bound for Network Navigability
SIAM Journal on Discrete Mathematics
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We consider the problem of determining constructions with an asymptotically optimal oblivious diameter in small world graphs under the Kleinberg’s model. In particular, we give the first general lower bound holding for any monotone distance distribution, that is induced by a monotone generating function. Namely, we prove that the expected oblivious diameter is Ω (log 2n) even on a path of n nodes. We then focus on deterministic constructions and after showing that the problem of minimizing the oblivious diameter is generally intractable, we give asymptotically optimal solutions, that is with a logarithmic oblivious diameter, for paths, trees and Cartesian products of graphs, including d-dimensional grids for any fixed value of d.