Randomized algorithms
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 protocol for internet applications
IEEE/ACM Transactions on Networking (TON)
Efficient Routing in Networks with Long Range Contacts
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
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
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Close to optimal decentralized routing in long-range contact networks
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Could any graph be turned into a small-world?
Theoretical Computer Science - Complex networks
Eclecticism shrinks even small worlds
Distributed Computing - Special issue: PODC 04
Universal augmentation schemes for network navigability: overcoming the √n-barrier
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
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
Asymptotically Optimal Solutions for Small World Graphs
Theory of Computing Systems
Degree-Optimal Routing for P2P Systems
Theory of Computing Systems
Greedy routing in tree-decomposed graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
How much independent should individual contacts be to form a small–world?
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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We study Small-World graphs in the perspective of their use in the development of efficient as well as easy to implement network infrastructures. Our analysis starts from the Small-World model proposed by Kleinberg: a grid network augmented with directed long-range random links. The choices of the long-range links are independent from one node to another. In this setting greedy routing and some of its variants have been analyzed and shown to produce paths of polylogarithmic expected length. We start from asking whether all the randomness, used in Kleinberg's model for establishing the long-range contacts of the nodes, is indeed necessary to assure the existence of short paths. In order to deal with the above question, we impose (stringent) restrictions on the choice of long-range links and we show that such restrictions do not increase the average path length of greedy routing and its variations. We are able to decrease the number of random bits, required to establish each node's long-range link, from @W(logn) to O(loglogn) on a network of size n. Diminishing the randomness in the choice of random links has several benefits; in particular, it implies an increase in the clustering of the graph, thus increasing the resilience of the network.