Randomized algorithms
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of 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
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Routing in Networks with Low Doubling Dimension
ICDCS '06 Proceedings of the 26th IEEE International Conference on Distributed Computing Systems
On Small World Graphs in Non-uniformly Distributed Key Spaces
ICDEW '05 Proceedings of the 21st International Conference on Data Engineering Workshops
Local embeddings of metric spaces
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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
Decentralized search in networks using homophily and degree disparity
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Greedy routing in tree-decomposed graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Polylogarithmic network navigability using compact metrics with small stretch
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Structured overlay for heterogeneous environments: Design and evaluation of oscar
ACM Transactions on Autonomous and Adaptive Systems (TAAS)
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Social networks support efficient decentralized search: people can collectively construct short paths to a specified target in the network. Rank-based friendship--where the probability that person u befriends person v is inversely proportional to the number of people who are closer to u than v is--is an empirically validated model of acquaintanceship that provably results in efficient decentralized search via greedy routing, even in networks with variable population densities. In this paper, we introduce cautious-greedy routing, a variant of greedy that avoids taking large jumps unless they make substantial progress towards the target. Our main result is that cautious-greedy routing finds a path of short expected length from an arbitrary source to a randomly chosen target, independent of the population densities. To quantify the expected length of the path, we define the depth of field of a metric space, a new quantity that intuitively measures the "width" of directions that leave a point in the space. Our main result is that cautious-greedy routing finds a path of expected length O(log2 n) in n-person networks that have aspect ratio polynomial in n, bounded doubling dimension, and bounded depth of field. Specifically, in k-dimensional grids under Manhattan distance with arbitrary population densities, the O(log2 n) expected path length that we achieve with the cautious-greedy algorithm improves the best previous bound of O(log3 n) with greedy routing.