🤖 AI Summary
This work addresses the Bandwidth Coloring Problem (BCP), which imposes a minimum separation constraint on colors assigned to adjacent vertices and has important applications in domains such as frequency assignment. The study presents a systematic investigation of SAT-based encodings for BCP, introducing a unified framework that encompasses single-variable, double-variable, and block encodings. For the first time in this context, symmetry-breaking constraints and an incremental solving strategy are incorporated. The proposed block encoding substantially enhances solver efficiency, achieving state-of-the-art performance on the GEOM and MS-CAP benchmarks. Notably, it proves the optimality of the GEOM120b instance within approximately 1,000 seconds—a result unattainable by prior methods even after one hour of computation.
📝 Abstract
The Bandwidth Coloring Problem (BCP) generalizes graph coloring by enforcing minimum separation constraints between adjacent vertices and arises in frequency assignment applications. While SAT-based approaches have shown promise for exact BCP solving, the encoding design space remains largely unexplored. This paper presents a systematic study of SAT encodings for the BCP, proposing a unified framework with six encoding methods across three categories: one-variable, two-variable, and block encodings. We evaluate the impact of key features including incremental solving and symmetry breaking. While symmetry breaking has been studied for graph coloring, it has not been systematically evaluated for SAT-based BCP solvers. Our analysis reveals significant interaction effects between encoding choices and solver configurations. The proposed framework achieves state-of-the-art performance on GEOM and MS-CAP benchmarks. Block encodings solve GEOM120b, the hardest instance, to proven optimality in approximately 1000 seconds, whereas previous methods could not solve it within a one-hour time limit.