Vertex Ordering Algorithms for Graph Coloring Problem

TL;DR

This paper explores how social network analytics metrics, especially closeness centrality, can optimize vertex ordering in greedy graph coloring algorithms, reducing the number of colors needed.

Contribution

It introduces the use of social network metrics for vertex ordering in graph coloring, demonstrating improved results with closeness centrality.

Findings

Closeness centrality-based ordering reduces color count.

Social network metrics influence vertex visit order.

Greedy algorithms benefit from centrality-based ordering.

Abstract

Graph coloring is a fundamental problem in combinatorics with many applications in practice. In this problem, the vertices in a given graph must be colored by using the least number of colors in such a way that a vertex has a different color than its neighbors. The problem, as well as its different variants, has been proven to be NP-Hard. Therefore, there are greedy algorithms in the literature aiming to use a small number of colors. These algorithms traverse the vertices and color them one by one. The vertex visit order has a significant impact on the number of colors used. In this work, we investigated if social network analytics metrics can be used to find this order. Our experiments showed that when closeness centrality is used to find vertex visit order, a smaller number of colors is used by the greedy algorithms.