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The diameter of a cycle plus a random matching
SIAM Journal on Discrete Mathematics
Probabilistic recurrence relations
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Randomized algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
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On power-law relationships of the Internet topology
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Small worlds: the dynamics of networks between order and randomness
Small worlds: the dynamics of networks between order and randomness
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A random graph model for massive graphs
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COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
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Information Processing Letters
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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
Close to optimal decentralized routing in long-range contact networks
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Theoretical Computer Science - Complex networks
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Theoretical Computer Science - Complex networks
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USITS'03 Proceedings of the 4th conference on USENIX Symposium on Internet Technologies and Systems - Volume 4
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ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Navigating low-dimensional and hierarchical population networks
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
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Efficient file search in non-DHT P2P networks
Computer Communications
Polylogarithmic network navigability using compact metrics with small stretch
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Recovering the Long-Range Links in Augmented Graphs
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Universal augmentation schemes for network navigability
Theoretical Computer Science
Tight lower bounds for greedy routing in uniform small world rings
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Navigable Small-World networks with few random bits
Theoretical Computer Science
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ACM Transactions on Autonomous and Adaptive Systems (TAAS)
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
Depth of field and cautious-greedy routing in social networks
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Peer to peer multidimensional overlays: approximating complex structures
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Small-world networks: from theoretical bounds to practical systems
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Oscar: small-world overlay for realistic key distributions
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Graph embedding through random walk for shortest paths problems
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
Biased selection for building small-world networks
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A Lower Bound for Network Navigability
SIAM Journal on Discrete Mathematics
Optimal path search in small worlds: dimension matters
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Near optimal routing in a small-world network with augmented local awareness
ISPA'05 Proceedings of the Third international conference on Parallel and Distributed Processing and Applications
Greedy routing in tree-decomposed graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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DISC'05 Proceedings of the 19th international conference on Distributed Computing
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ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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We investigate the notion of Long Range Contact graphs. Roughly speaking, such a graph is defined by (1) an underlying network topology G, and (2) one (or possibly more) extra link connecting every node u to a "long distance" neighbor, called the long range contact of u. This extra link represents the a priori knowledge that a node has about far nodes and is set up randomly according to some probability distributions p. To illustrate the claim that Long Range Contact graphs are a good model for the small world phenomenon, we study greedy routing in these graphs. Greedy routing is the distributed routing protocol in which a node u makes use of its long range contact to progress toward a target, if this contact is closer to the target, than the other neighbors. We give upper and lower bounds on greedy routing on the n-node ring Cn augmented with links chosen using the r-harmonic distributions. In particular, we show a tight 驴(log2 n)-bound for the expected number of steps required for routing in Cn augmented using the 1-harmonic distribution. Hence, our study shows that the model of Kleinberg [11] can be simplified by using the ring rather than the mesh while preserving the main features of the model. Our study also demonstrates the significant difference (in term of both diameter and routing) between the ring augmented with long range contacts chosen with the harmonic distribution and the ring augmented with a random matching as introduced by Bollobas and Chung [3]. Finally, using epimorphisms of a graph onto another, for any network G, we show how to define a probability distribution p and study the performance of greedy routing in G augmented with p. For appropriate embeddings (if they exist), this performance turns out to be O(log2 n).