Optimized Graph Coloring Algorithms for Large-Scale Networks: A Comparative Analysis of Heuristic and Exact Methods

Abstract

The graph coloring problem serves as a basic graph theoretical construct that finds applications throughout network optimization together with scheduling needs and register allocation and resource administration. This research document offers an evaluation of contemporary heuristic solutions together with exact methods for solving large-scale network graph coloring problems. We assess different algorithms which incorporate greedy approaches together with meta-heuristics and integer programming formulations in terms of their ability to perform and scale while maintaining high solution quality. Exact methods excel at finding optimal solutions for small to medium network instances yet heuristic methods become essential for large-scale instances because exact methods run out of practical computing capability. When addressing real-world network applications hybrid approaches of local search integrated with population-based meta-heuristics deliver the optimal equilibrium between solution quality and computing efficiency.