It has been established in the fields of computer science and physics that many NP-hard and NP-complete graph-theoretic problems can be formulated and solved as Ising spin models. We discuss several problems that have a history in mathematical psychology, most notably max-cut clustering, graph coloring, a linear ordering problem related to paired comparison ranking and directed acyclic graphs, and the problem of finding a minimum subset of points necessary to contain another point within a convex hull. New Ising spin models are presented for the latter two problems. Additionally, we provide MATLAB software programs for obtaining solutions via enumeration of all spin ensembles (when computationally feasible) and simulated annealing. We are not claiming that the Ising spin model should be the preferred approach for formulating and solving graph-theoretic problems on conventional digital computers but it does provide a unifying framework for these problems, which may lead to future computational improvements. Recent progress in the development of quantum computing architecture has shown that Ising spin models can afford enormous improvements in algorithm efficiency when implemented on these platforms, potentially leading to widespread use of the methodology in the future.

在计算机科学和物理学领域已经确定，可以将许多NP硬和NP完备的图论问题公式化并解决为Ising自旋模型。我们讨论了数学心理学中历史悠久的几个问题，最著名的是最大割聚类，图着色，与成对的比较排名和有向无环图有关的线性排序问题，以及寻找包含另一个点的最小点子集的问题在凸包内。针对后两个问题提出了新的伊辛自旋模型。此外，我们提供了MATLAB软件程序，用于通过枚举所有自旋合奏（在计算上可行的情况下）和模拟退火来获得解决方案。我们并没有声称Ising自旋模型应该是在常规数字计算机上公式化和解决图形理论问题的首选方法，但是它确实为这些问题提供了统一的框架，这可能会导致未来的计算改进。量子计算体系结构开发的最新进展表明，在这些平台上实现伊辛自旋模型可以极大地提高算法效率，从而有可能导致该方法在未来的广泛使用。