Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Finding nearest neighbors in growth-restricted metrics
STOC '02 Proceedings of the thiry-fourth 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
Efficient Routing in Networks with Long Range Contacts
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
LAND: stretch (1 + ε) locality-aware networks for DHTs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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
On the bias of traceroute sampling: or, power-law degree distributions in regular graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Analyzing and characterizing small-world graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Evolution and Structure of the Internet: A Statistical Physics Approach
Evolution and Structure of the Internet: A Statistical Physics Approach
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
Could any graph be turned into a small-world?
Theoretical Computer Science - Complex networks
Object location using path separators
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
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
Navigating low-dimensional and hierarchical population networks
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Greedy routing in tree-decomposed graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Asymptotically optimal solutions for small world graphs
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Distributed social graph embedding
Proceedings of the 20th ACM international conference on Information and knowledge management
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The augmented graphmodel, as introduced by Kleinberg (STOC 2000), is an appealing model for analyzing navigability in social networks. Informally, this model is defined by a pair (H,φ), where His a graph in which inter-node distances are supposed to be easy to compute or at least easy to estimate. This graph is "augmented" by links, called long-rangelinks, which are selected according to the probability distribution φ. The augmented graph model enables the analysis of greedy routingin augmented graphs G茂戮驴 (H,φ). In greedy routing, each intermediate node handling a message for a target tselects among all its neighbors in Gthe one that is the closest to tin Hand forwards the message to it.This paper addresses the problem of checking whether a given graph Gis an augmented graph. It answers part of the questions raised by Kleinberg in his Problem 9 (Int. Congress of Math. 2006). More precisely, given G茂戮驴 (H,φ), we aim at extracting the base graph Hand the long-range links Rout of G. We prove that if Hhas high clustering coefficient and Hhas bounded doubling dimension, then a simple local maximum likelihood algorithm enables to partition the edges of Ginto two sets H茂戮驴 and R茂戮驴 such that E(H) 茂戮驴 H茂戮驴 and the edges in H茂戮驴 茂戮驴 E(H) are of small stretch, i.e., the map His not perturbed too greatly by undetected long-range links remaining in H茂戮驴. The perturbation is actually so small that we can prove that the expected performances of greedy routing in Gusing the distances in H茂戮驴 are close to the expected performances of greedy routing using the distances in H. Although this latter result may appear intuitively straightforward, since H茂戮驴 茂戮驴 E(H), it is not, as we also show that routing with a map more precise than Hmay actually damage greedy routing significantly. Finally, we show that in absence of a hypothesis regarding the high clustering coefficient, any local maximum likelihood algorithm extracting the long-range links can miss the detection of at least 茂戮驴(n5茂戮驴/logn) long-range links of stretch at least 茂戮驴(n1/5 茂戮驴 茂戮驴) for any 0 茂戮驴Hcannot be recovered with good accuracy.