The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Fault-tolerant routing in peer-to-peer systems
Proceedings of the twenty-first annual symposium on Principles of distributed 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
The impact of DHT routing geometry on resilience and proximity
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SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic analysis of a basic evolutionary algorithm for continuous optimization
Theoretical Computer Science
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
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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
Small worlds as navigable augmented networks: model, analysis, and validation
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Asymptotically optimal solutions for small world graphs
DISC'05 Proceedings of the 19th international conference on Distributed Computing
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
Brief announcement: tight lower bounds for greedy routing in uniform small world rings
Proceedings of the 28th ACM symposium on Principles of distributed computing
On the searchability of small-world networks with arbitrary underlying structure
Proceedings of the forty-second ACM symposium on Theory of computing
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We consider augmented ring-based networks with vertices 0,...,n-1, where each vertex is connected to its left and right neighbor and possibly to some further vertices (called long range contacts). The outgoing edges of a vertex v are obtained by choosing a subset D of {1,2,...n-1}, with 1, n-1 in D, at random according to a probability distribution mu on all such D and then for each i in D connecting v to (v+i) mod n by a unidirectional link. The choices for different v are done independently and uniformly in the sense that the same distribution mu is used for all v. The expected number of long range contacts is l=E(|D|)-2. Motivated by Kleinberg's (2000) Small World Graph model and packet routing strategies for peer-to-peer networks, the greedy routing algorithm on augmented rings, where a packet sitting in a node v is routed to the neighbor of v closest to the destination of the package, has been investigated thoroughly, both for the "one-sided case", where packets can travel only in one direction, and the "two-sided case", where there is no such restriction. In this paper, for both the one-sided and the two-sided case and for an arbitrary distribution mu, we prove a lower bound of Omega((log n)2/l) on the expected number of hops that are needed by the greedy strategy to route a package between two randomly chosen vertices on the ring. This bound is tight for Omega(1)