Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Informative Labeling Schemes for Graphs
Informative Labeling Schemes for Graphs
Improved Compact Routing Scheme for Chordal Graphs
DISC '02 Proceedings of the 16th International Conference on Distributed Computing
A Space Lower Bound for Routing in Trees
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Labeling Schemes for Dynamic Tree Networks
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
On Majority Voting Games in Trees
SOFSEM '01 Proceedings of the 28th Conference on Current Trends in Theory and Practice of Informatics Piestany: Theory and Practice of Informatics
Engineering Tree Labeling Schemes: A Case Study on Least Common Ancestors
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
As Good as It Gets: Competitive Fault Tolerance in Network Structures
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Compact ancestry labeling schemes for XML trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A note on labeling schemes for graph connectivity
Information Processing Letters
Compact encodings for all local path information in web taxonomies with application to wordnet
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
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
Controller and estimator for dynamic networks
Information and Computation
| Hi-index | 0.00 |
This paper introduces and studies the notion of informative labeling schemes for arbitrary graphs. Let f(W) be a function on subsets of vertices W. An f labeling scheme labels the vertices of a weighted graph G in such a way that f(W) can be inferred efficiently for any vertex subset W of G by merely inspecting the labels of the vertices of W, without having to use any additional information sources. The paper develops f labeling schemes for some functions f over the class of n-vertex trees, including SepLevel, the separation level of any two vertices in the tree, LCA, the least common ancestor of any two vertices, and Center, the center of any three given vertices in the tree. These schemes use O(log2 n)-bit labels, which is asymptotically optimal. We then turn to weighted graphs and consider the function Steiner(W), denoting the weight of the Steiner tree spanning the vertices of W in the graph. For n-vertex weighted trees with M-bit edge weights, it is shown that there exists a Steiner labeling scheme using O((M+log n) log n) bit labels, which is asymptotically optimal. In the full paper it is shown that for the class of arbitrary n-vertex graphs with M-bit edge weights, there exists an approximate-Steiner labeling scheme, providing an estimate (up to a logarithmic factor) for Steiner(W) using O((M +log n) log2 n) bit labels.