Token management schemes and random walks yield self-stabilizing mutual exclusion
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
Randomized algorithms
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Spatial gossip and resource location protocols
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Search and replication in unstructured peer-to-peer networks
ICS '02 Proceedings of the 16th international conference on Supercomputing
Peer-to-Peer Membership Management for Gossip-Based Protocols
IEEE Transactions on Computers
Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
Simple efficient load balancing algorithms for peer-to-peer systems
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Vivaldi: a decentralized network coordinate system
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
Mercury: supporting scalable multi-attribute range queries
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
Labeling Schemes for Flow and Connectivity
SIAM Journal on Computing
Journal of Algorithms
Journal of the ACM (JACM)
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Meridian: a lightweight network location service without virtual coordinates
Proceedings of the 2005 conference on Applications, technologies, architectures, and protocols for computer communications
Metric Embeddings with Relaxed Guarantees
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Random Walk for Self-Stabilizing Group Communication in Ad Hoc Networks
IEEE Transactions on Mobile Computing
ICDCS '07 Proceedings of the 27th International Conference on Distributed Computing Systems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Towards fast decentralized construction of locality-aware overlay networks
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Efficient distributed approximation algorithms via probabilistic tree embeddings
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Labeling Schemes for Tree Representation
Algorithmica
Quickly routing searches without having to move content
IPTPS'05 Proceedings of the 4th international conference on Peer-to-Peer Systems
Optimal distributed all pairs shortest paths and applications
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Fast routing table construction using small messages: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Distance computation (e.g., computing shortest paths) is one of the most fundamental primitives used in communication networks. The cost of effectively and accurately computing pairwise network distances can become prohibitive in large-scale networks such as the Internet and Peer-to-Peer (P2P) networks. To negotiate the rising need for very efficient distance computation at scales never imagined before, approximation techniques for numerous variants of this question have recently received significant attention in the literature. Several different areas of theoretical research have emerged centered around this problem, such as metric embeddings, distance labelings, spanners, and distance oracles. The goal is to preprocess the graph and store a small amount of information such that whenever a query for any pairwise distance is issued, the distance can be well approximated (i.e., with small stretch) very quickly in an online fashion. Specifically, the pre-processing (usually) involves storing a small sketch with each node, such that at query time only the sketches of the concerned nodes need to be looked up to compute the approximate distance. Techniques derived from metric embeddings have been considered extensively by the networking community, usually under the name of network coordinate systems. On the other hand, while the computation of distance oracles has received considerable attention in the context of web graphs and social networks, there has been little work towards similar algorithms within the networking community. In this paper, we present the first theoretical study of distance sketches derived from distance oracles in a distributed network. We first present a fast distributed algorithm for computing approximate distance sketches, based on a distributed implementation of the distance oracle scheme of [Thorup-Zwick, JACM 2005]. We also show how to modify this basic construction to achieve different tradeoffs between the number of pairs for which the distance estimate is accurate, the size of the sketches, and the time and message complexity necessary to compute them. These tradeoffs can then be combined to give an efficient construction of small sketches with provable average-case as well as worst-case performance. Our algorithms use only small-sized messages and hence are suitable for bandwidth-constrained networks, and can be used in various networking applications such as topology discovery and construction, token management, load balancing, monitoring overlays, and several other problems in distributed algorithms.