Degree-Based Logical Adjacency Checking (DBLAC): A Novel Heuristic for Vertex Coloring

TL;DR

This paper introduces DBLAC, a new heuristic for vertex coloring that uses logical AND operations to improve efficiency and reduce colors, supported by theoretical analysis and experimental comparisons.

Contribution

The paper presents a novel degree-based heuristic, DBLAC, with detailed complexity analysis and competitive performance against established algorithms.

Findings

DBLAC achieves fewer colors than some existing heuristics.

DBLAC demonstrates competitive runtime performance.

Theoretical analysis confirms efficiency of DBLAC.

Abstract

Degree Based Logical Adjacency Checking (DBLAC). An efficient coloring of graphs with unique logical AND operations. The logical AND operation shows more effective color assignment and fewer number of induced colors in the case of common edges between vertices. In this work, we provide a detailed theoretical analysis of DBLAC's time and space complexity. It furthermore shows its effectiveness through prolonged experiments on standard benchmark graphs. We compare it with existing algorithms, namely DSATUR and Recursive Largest First (RLF). Second, we show how DBLAC achieves competitive results with respect to both the number of colors used and runtime performance.