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
Journal of Algorithms
Journal of the ACM (JACM)
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
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
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
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of 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
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
Graph Augmentation via Metric Embedding
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Universal augmentation schemes for network navigability
Theoretical Computer Science
Graph embedding through random walk for shortest paths problems
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
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Graph augmentation theory is a general framework for analyzing navigability in social networks. It is known that, for large classes of graphs, there exist augmentations of these graphs such that greedy routing according to the shortest path metric performs in polylogarithmic expected number of steps. However, it is also known that there are classes of graphs for which no augmentations can enable greedy routing according to the shortest path metric to perform better than Ω(n1/√log n) expected number of steps. In fact, the best known universal bound on the greedy diameter of arbitrary graph is essentially n1/3. That is, for any graph, there is an augmentation such that greedy routing according to the shortest path metric performs in Õ(n1/3) expected number of steps. Hence, greedy routing according to the shortest path metric has at least two drawbacks. First, it is in general space-consuming to encode locally the shortest path distances to all the other nodes, and, second, greedy routing according to the shortest path metric performs poorly in some graphs. We prove that, using semimetrics of small stretch results in a huge positive impact, in both encoding space and efficiency of greedy routing. More precisely, we show that, for any connected n-node graph G and any integer k ≥ 1, there exist an augmentation φ of G and a semimetric μ on G with stretch 2/k-1 such that greedy routing according to μ performs in O(k2 n2/klog2n) expected number of steps. As a corollary, we get that for any connected n-node graph G, there exist an augmentation φ of G and a semimetric μ on G with stretch O(log n) such that greedy routing according to μ performs in polylogarithmic expected number of steps. This latter semimetric can be encoded locally at every node using only a polylogarithmic number of bits.