A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Graph classes: a survey
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
Efficient Routing in Networks with Long Range Contacts
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
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
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed 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
A doubling dimension threshold θ(loglogn) for augmented graph navigability
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
Polylogarithmic network navigability using compact metrics with small stretch
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Recovering the Long-Range Links in Augmented Graphs
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Graph Augmentation via Metric Embedding
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Tight lower bounds for greedy routing in uniform small world rings
Proceedings of the forty-first annual ACM symposium on Theory of computing
Navigable Small-World networks with few random bits
Theoretical Computer Science
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
On the searchability of small-world networks with arbitrary underlying structure
Proceedings of the forty-second ACM symposium on Theory of computing
Graph embedding through random walk for shortest paths problems
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
A Lower Bound for Network Navigability
SIAM Journal on Discrete Mathematics
Sub-linear universal spatial gossip protocols
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
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Augmented graphs were introduced for the purpose of analyzing the "six degrees of separation between individuals" observed experimentally by the sociologist Standley Milgram in the 60's. Formally, an augmented graph is a pair (G,φ) where G is a graph, and φ is a collection of probability distributions {φu, u ∈ V(G)}. Every node u ∈ V(G) is given an extra link, called a long range link, pointing to some node v, called the long range contact of u. The head v of this link is chosen at random by Pr{u → v} = φu(v). In augmented graphs, greedy routing is the oblivious routing process in which every intermediate node chooses among all its neighbors (including its long range contact) the one that is closest to the target according to the distance measured in the underlying graph G, and forwards to it. Roughly, augmented graphs aim at modeling the structure of social networks, while greedy routing aims at modeling the searching procedure applied in Milgram's experiment. Our objective is to design efficient universal augmentation schemes, i.e., augmentation schemes that give to any graph G a collection of probability distributions φ such that greedy routing in (G,φ) is fast. It is known that the uniform scheme φunif is a universal scheme ensuring that, for any n-node graph G, greedy routing in (G,φunif) performs in O(√n) expected number of steps. Our main result is the design of a universal augmentation scheme φ such that greedy routing in (G,φ) performs in Õ(n1/3) expected number of steps for any n-node graph G. We also show that under some more restricted model, the √n-barrier cannot be overcome.