Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
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SIAM Journal on Computing
Routing with polynomial communication-space trade-off
SIAM Journal on Discrete Mathematics
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Labeling Schemes for Dynamic Tree Networks
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Approximate Distance Labeling Schemes
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Engineering Tree Labeling Schemes: A Case Study on Least Common Ancestors
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
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SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
An Optimal Labeling for Node Connectivity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Forbidden-set distance labels for graphs of bounded doubling dimension
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Compact ancestry labeling schemes for XML trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Exact distance labelings yield additive-stretch compact routing schemes
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Max-stretch reduction for tree spanners
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
A dynamic implicit adjacency labelling scheme for line graphs
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
General compact labeling schemes for dynamic trees
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Constructing labeling schemes through universal matrices
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Labeling schemes for vertex connectivity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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This paper considers informative labeling schemes for graphs. Specifically, the question introduced is whether it is possible to label the vertices of a graph with short labels in such a way that the distance between any two vertices can be inferred from inspecting their labels. A labeling scheme enjoying this property is termed a proximity-preserving labeling scheme. It is shown that for the class of n-vertex weighted trees with M-bit edge weights, there exists such a proximity-preserving labeling scheme using O(M log n + log2n) bit labels. For the family of all n-vertex unweighted graphs, a labeling scheme is proposed that using O(log2 n ċ ϰ ċ n1/ϰ) bit labels can provide approximate estimates to the distance, which are accurate up to a factor of √8ϰ. In particular, using O(log3 n) bit labels the scheme can provide estimates accurate up to a factor of √2 log n. (For weighted graphs, one of the log n factors in the label size is replaced by a factor logarithmic in the network's diameter.) In addition to their theoretical interest, proximity-preserving labeling systems seem to have some relevance in the context of communication networks. We illustrate this by proposing a potential application of our labeling schemes to efficient distributed connection setup in circuit-switched networks.