On local representation of distances in trees
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Engineering Tree Labeling Schemes: A Case Study on Least Common Ancestors
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
On randomized representations of graphs using short labels
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
An Optimal Labeling for Node Connectivity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Labeling schemes for vertex connectivity
ACM Transactions on Algorithms (TALG)
Shorter implicit representation for planar graphs and bounded treewidth graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Distributed relationship schemes for trees
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Short labels by traversal and jumping
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
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We consider labeling schemes for trees, supporting various relationships between nodes at small distance. For instance, we show that given a tree T and an integer k we can assign labels to each node of T such that given the label of two nodes we can decide, from these two labels alone, if the distance between v and w is at most k and, if so, compute it. For trees with n nodes and $k\geq 2$, we give a lower bound on the maximum label length of $\log n + \Omega(\log \log n)$ bits, and for constant k, we give an upper bound of log n + O(log log n). Bounds for ancestor, sibling, connectivity, and bi- and triconnectivity labeling schemes are also presented.