Distance and routing labeling schemes for cube-free median graphs

TL;DR

This paper demonstrates that cube-free median graphs admit efficient distance and routing labeling schemes with labels of size proportional to the cube of the logarithm of the number of nodes, enabling quick distance and routing computations.

Contribution

The paper establishes that cube-free median graphs support distance and routing labeling schemes with labels of size O(log^3 n), a significant step for this class of graphs.

Findings

Distance and routing labels of size O(log^3 n) for cube-free median graphs.

Efficient distance and routing computations using these labels.

Advancement in labeling schemes for specific graph classes.

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 $u$ and $v$ can be determined efficiently by merely inspecting the labels of $u$ and $v$, without using any other information. Similarly, routing labeling schemes label the vertices of a graph in a such a way that given the labels of a source node and a destination node, it is possible to compute efficiently the port number of the edge from the source that heads in the direction of the destination. One of important problems is finding natural classes of graphs admitting distance and/or routing labeling schemes with labels of polylogarithmic size. In this paper, we show that the class of cube-free median graphs on $n$ nodes enjoys distance and routing labeling schemes with labels of $O(\log^3 n)$ bits.