Distributed recoloring of interval and chordal graphs

TL;DR

This paper investigates distributed recoloring algorithms for interval and chordal graphs, addressing the transformation between two colorings in these specific graph classes, which are more representative of real networks.

Contribution

It introduces the study of distributed recoloring specifically for interval and chordal graphs, combining two recent research directions in graph coloring.

Findings

Addresses distributed recoloring in interval graphs

Addresses distributed recoloring in chordal graphs

Extends understanding of coloring transformations in specific graph classes

Abstract

One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions. First, the problem of recoloring, that is computing an efficient transformation between two given colorings (instead of computing a new coloring), has been considered, both to model radio network updates, and as a useful subroutine for coloring. Second, as it appears that general graphs and bounded-degree graphs do not model real networks very well (with, respectively, pathological worst-case topologies and too strong assumptions), coloring has been studied in more specific graph classes. In this paper, we study the intersection of these two directions: distributed recoloring in two relevant graph classes, interval and chordal graphs.