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
Short paths in expander graphs
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of 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
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
Approximation Schemes for First-Order Definable Optimisation Problems
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
A doubling dimension threshold θ(loglogn) for augmented graph navigability
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Asymptotically Optimal Solutions for Small World Graphs
Theory of Computing Systems
Polylogarithmic network navigability using compact metrics with small stretch
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Greedy routing in tree-decomposed graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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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. We define an augmented graph as a pair (G,M) where G is an n-node graph with nodes labeled in {1,...,n}, and M is an nxn stochastic matrix. 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}=M"u","v. In augmented graphs, greedy routing is the oblivious routing process in which every intermediate node chooses from 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. The best augmentation scheme known so far ensures that, for any n-node graph G, greedy routing performs in O(n) expected number of steps. Our main result is the design of an augmentation scheme that overcomes the O(n) barrier. Precisely, we prove that for any n-node graph G whose nodes are arbitrarily labeled in {1,...,n}, there exists a stochastic matrix M such that greedy routing in (G,M) performs in O@?(n^1^/^3), where the O@? notation ignores the polylogarithmic factors. We prove additional results when the stochastic matrix M is universal to all graphs. In particular, we prove that the O(n) barrier can still be overcame for large graph classes even if the matrix M is universal. This however requires an appropriate labeling of the nodes. If the node labeling is arbitrary, then we prove that the O(n) barrier cannot be overcome with universal matrices.