Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Distance Labeling Schemes for Well-Separated Graph Classes
Distance Labeling Schemes for Well-Separated Graph Classes
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
Localized and compact data-structure for comparability graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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
The exact distance to destination in undirected world
The VLDB Journal — The International Journal on Very Large Data Bases
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Distance labeling schemes are schemes that 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. It is shown in this paper that the classes of interval graphs and permutation graphs enjoy such a distance labeling scheme using O(log2 n) bit labels on n- vertex graphs. Towards establishing these results, we present a general property for graphs, called well-(α, g)-separation, and show that graph classes satisfying this property have O(g(n) ċ log n) bit labeling schemes. In particular, interval graphs are well-(2, log n)-separated and permutation graphs are well-(6, log n)-separated.