The diameter of a cycle plus a random matching
SIAM Journal on Discrete Mathematics
Probabilistic recurrence relations
Journal of the ACM (JACM)
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Spatial gossip and resource location protocols
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Regular Article: The Diameter of Sparse Random Graphs
Advances in Applied Mathematics
The diameter of long-range percolation clusters on finite cycles
Random Structures & Algorithms
Viceroy: a scalable and dynamic emulation of the butterfly
Proceedings of the twenty-first annual symposium on Principles of distributed 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
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
Tradeoffs between stretch factor and load balancing ratio in routing on growth restricted graphs
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Could any graph be turned into a small-world?
Theoretical Computer Science - Complex networks
Navigating low-dimensional and hierarchical population networks
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Polylogarithmic network navigability using compact metrics with small stretch
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Opportunistic spatial gossip over mobile social networks
Proceedings of the first workshop on Online social networks
Recovering the Long-Range Links in Augmented Graphs
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Universal augmentation schemes for network navigability
Theoretical Computer Science
Unsupervised creation of small world networks for the preservation of digital objects
Proceedings of the 9th ACM/IEEE-CS joint conference on Digital libraries
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
Non-searchability of random power-law graphs
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
On the searchability of small-world networks with arbitrary underlying structure
Proceedings of the forty-second ACM symposium on Theory of computing
Optimal path search in small worlds: dimension matters
Proceedings of the forty-third annual ACM symposium on Theory of computing
Near optimal routing in a small-world network with augmented local awareness
ISPA'05 Proceedings of the Third international conference on Parallel and Distributed Processing and Applications
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
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We study variants of Kleinberg's small-world model where we start with a k-dimensional grid and add a random directed edge from each node. The probability u's random edge is to v is proportional to d(u,v)-r where d(u,v) is the lattice distance and r is a parameter of the model.For a k-dimensional grid, we show that these graphs have poly-log expected diameter when k r k, but have polynomial expected diameter when r 2k. This shows an interesting phase-transition between small-world and "large-world" graphs.We also present a general framework to construct classes of small-world graphs with Θ(log n) expected diameter, which includes several existing settings such as Kleinberg's grid-based and tree-based settings [15].We also generalize the idea of 'adding links with probability α the inverse distance' to design small-world graphs. We use semi-metric and metric functions to abstract distance to create a class of random graphs where almost all pairs of nodes are connected by a path of length O (log n), and using only local information we can find paths of poly-log length.