Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Universal graphs and induced-universal graphs
Journal of Graph Theory
Compact labeling schemes for ancestor queries
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Labeling schemes for small distances in trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Small Induced-Universal Graphs and Compact Implicit Graph Representations
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Compact and localized distributed data structures
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Journal of Algorithms
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Labeling Schemes for Small Distances in Trees
SIAM Journal on Discrete Mathematics
Compact Labeling Scheme for Ancestor Queries
SIAM Journal on Computing
Distance and routing labeling schemes for non-positively curved plane graphs
Journal of Algorithms
Reconstructing approximate tree metrics
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Distance labeling in hyperbolic graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Localized and compact data-structure for comparability graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
On compact and efficient routing in certain graph classes
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Constructing labeling schemes through universal matrices
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Compact separator decompositions in dynamic trees and applications to labeling schemes
DISC'07 Proceedings of the 21st international conference on 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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We consider a distributed representation scheme for trees, supporting some special relationships between nodes at small distance. For instance, we show that for a tree T and an integer k we can assign local information on nodes such that we can decide for any two nodes u and v if the distance between u and v is at most k and if so, compute it only using the local information assigned. For trees with n nodes, the local information assigned by our scheme are binary labels of log n+O(k log(k log(n/k))) bits, improving the results of Alstrup, Bille, and Rauhe (SODA '03).