Graph Coloring: Comparing Cluster Graphs to Factor Graphs

TL;DR

This paper introduces a novel approach to graph coloring using cluster graphs instead of the traditional factor graphs, along with an algorithm for constructing valid cluster graphs, demonstrating improved accuracy and efficiency.

Contribution

The paper proposes a new cluster graph formulation for graph coloring and introduces the LTRIP algorithm for automatic cluster graph construction, showing advantages over factor graphs.

Findings

Cluster graphs outperform factor graphs in accuracy.

Cluster graphs are more computationally efficient.

LTRIP algorithm effectively constructs valid cluster graphs.

Abstract

We present a means of formulating and solving graph coloring problems with probabilistic graphical models. In contrast to the prevalent literature that uses factor graphs for this purpose, we instead approach it from a cluster graph perspective. Since there seems to be a lack of algorithms to automatically construct valid cluster graphs, we provide such an algorithm (termed LTRIP). Our experiments indicate a significant advantage for preferring cluster graphs over factor graphs, both in terms of accuracy as well as computational efficiency.