Ising-Machine-Based Solver for Constrained Graph Coloring Problems

Ising machines can find optimum or quasi-optimum solutions of combinatorial optimization problems efficiently and effectively. The graph coloring problem, which is one the difficult problems, to assign a color each vertex such that no two vertices connected by an edge have same color. Although methods map problem onto model quadratic unconstrained binary (QUBO) are proposed, none them considers minimizing number colors. In addition, there Ising-machine-based method considering additional constraints in order apply practical problems. this paper, we propose mapping including colors QUBO model. As well as constraint terms for firstly objective function term minimize so used spins cannot increase exponentially. Secondly, terms: One specific be colored with specified colors; other more than times given advance. We theoretically prove that, if energy proposed minimized, all satisfied minimized. result experiment using machine showed reduces up 75.1% on average compared existing baseline when not considered. Considering constraints, effectively feasible satisfying constraints.