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
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
ISPAN '05 Proceedings of the 8th International Symposium on Parallel Architectures,Algorithms and Networks
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
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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 independence assumed in the Kleinberg's model among long–range contacts of different 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 of its variations. 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.