Distance labeling schemes for $K_4$-free bridged graphs

Abstract

k-Approximate distance labeling schemes are schemes that label the vertices of a graph with short labels in such a way that the k-approximation of the distance between any two vertices u and v can be determined efficiently by merely inspecting the labels of u and v, without using any other information. One of the important problems is finding natural classes of graphs admitting exact or approximate distance labeling schemes with labels of polylogarithmic size. In this paper, we describe an approximate distance labeling scheme for the class of K4-free bridged graphs. This scheme uses labels of poly-logarithmic length O(log n 3 ) allowing a constant decoding time. Given the labels of two vertices u and v, the decoding function returns a value between the exact distance dG(u, v) and its quadruple 4dG(u, v).