On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
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
The diameter of a long-range percolation graph
Random Structures & Algorithms
Efficient Routing in Networks with Long Range Contacts
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Linear Time Solvable Optimization Problems on Graphs of Bounded Clique Width
WG '98 Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science
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
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
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
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
Eclecticism shrinks even small worlds
Distributed Computing - Special issue: PODC 04
Measurement based analysis, modeling, and synthesis of the internet delay space
Proceedings of the 6th ACM SIGCOMM conference on Internet measurement
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
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
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
INFOCOM'96 Proceedings of the Fifteenth annual joint conference of the IEEE computer and communications societies conference on The conference on computer communications - Volume 2
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
Papillon: greedy routing in rings
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Polylogarithmic network navigability using compact metrics with small stretch
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Distance graphs: from random geometric graphs to Bernoulli graphs and between
Proceedings of the fifth international workshop on Foundations of mobile computing
Tight lower bounds for greedy routing in uniform small world rings
Proceedings of the forty-first annual ACM symposium on Theory of 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
Navigating in a Graph by Aid of Its Spanning Tree Metric
SIAM Journal on Discrete Mathematics
Hi-index | 0.00 |
The small world phenomenon, a.k.a. the six degree of separation between individuals, was identified by Stanley Milgram at the end of the 60s. Milgram experiment demonstrated that letters from arbitrary sources and bound to an arbitrary target can be transmitted along short chains of closely related individuals, based solely on some characteristics of the target (professional occupation, state of leaving, etc.). In his paper on small world navigability, Jon Kleinberg modeled this phenomenon in the framework of augmented networks, and analyzed the performances of greedy routing in augmented multi-dimensional meshes. This paper objective is to survey the results that followed up Kleinberg seminal work, including results about: - extensions of the augmented network model, and variants of greedy routing, - designs of polylog-navigable graph classes, - the quest for universal augmentation schemes, and - discussions on the validation of the model in the framework of doubling metrics.