Distance labeling schemes for well-separated graph classes

Authors:
Michal Katz;Nir A. Katz;David Peleg
Affiliations:
Department of Applied Mathematics, Bar Ilan University, Ramat Gan 52900, Israel;Department of Applied Mathematics, Bar Ilan University, Ramat Gan 52900, Israel;Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel
Venue:
Discrete Applied Mathematics
Year:
2005

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Abstract

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) log n) bit labeling schemes. In particular, interval graphs are well-(2, log n)-separated and permutation graphs are well-(6, log n)-separated.