Distance labeling scheme and split decomposition

A distance labeling scheme is a distributed data-structure designed to answer queries about distance between any two vertices of a graph G. The data-structure consists in a label L(x,G) assigned to each vertex x of G such that the distance dG(x, y) between any two vertices x and y can be estimated as a function f(L(x,G), L(y,G)). In this paper, by the use of split decomposition of graphs, we combine several types of distance labeling schemes. This yields to optimal label length schemes for the family of distance-hereditary graphs and for other families of graphs, allowing distance estimation in constant time once the labels have been constructed.