Distance labeling schemes for well-separated graph classes

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.