A note on the height of binary search trees
Journal of the ACM (JACM)
Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Tree Contractions and Evolutionary Trees
SIAM Journal on Computing
A few logs suffice to build (almost) all trees: part II
Theoretical Computer Science
Height in a digital search tree and the longest phrase of the Lempel-Ziv scheme
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Nearest common ancestors: a survey and a new distributed algorithm
Proceedings of the fourteenth 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
The height of a random binary search tree
Journal of the ACM (JACM)
Compact and localized distributed data structures
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Coding the vertexes of a graph
IEEE Transactions on Information Theory
On the Complexity of Finite Sequences
IEEE Transactions on Information Theory
An Optimal Labeling for Node Connectivity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
| Hi-index | 5.23 |
We study how to label the vertices of a tree in such a way that we can decide the distance of two vertices in the tree given only their labels. Gavoille et al. proved that for any such distance labelling scheme, the maximum label length is at least 18log^2n-O(logn) bits, where n is the number of vertices in the input tree T. They also gave a separator-based labelling scheme that has the optimal label length @Q(logn@?log(H"n(T))), where H"n(T) is the height of T. We present two distance labelling schemes, namely, the backbone-based scheme and rake-based scheme, which also achieve the optimal label length. The two schemes always perform at least as well as the separator scheme. Furthermore, the rake-based scheme has a much smaller expected label length under certain tree distributions. With these new schemes, we also can find the least common ancestor of any two vertices based on their labels only.