符号网络中挫折指数的建模与计算研究
A modelling and computational study of the frustration index in signed networks
摘要：
计算符号图的挫折指数是解决包括社交网络、政治学、物理学、化学和生物学在内的许多领域问题的关键一步。挫折指数决定了网络与总体结构平衡状态的距离。虽然挫折指数的定义可以追溯到20世纪50年代，但它的精确算法计算，这是密切相关的经典NP-hard图问题，只是在最近几年才成为一个焦点。我们开发了三个新的二进制线性规划模型来计算挫折指数准确和有效的解决方案的全局优化问题。通过在Guesthouse中使用优先级分支和有效不等式求解模型，我们可以在不到一分钟的时间内在廉价的硬件上计算出具有超过15000条边的实签名网络的挫折指数。我们提供了广泛的随机和真实的签名网络的性能分析，并表明我们的模型优于所有现有的方法的大因素。基于求解时间，算法输出，和有效分支因子，我们突出了我们的模型的优越性，在文献中的精确和探试法。
英文摘要：
Computing the frustration index of a signed graph is a key step toward solving problems in many fields including social networks, political science, physics, chemistry, and biology. The frustration index determines the distance of a network from a state of total structural balance. Although the definition of the frustration index goes back to the 1950's, its exact algorithmic computation, which is closely related to classic NP-hard graph problems, has only become a focus in recent years. We develop three new binary linear programming models to compute the frustration index exactly and efficiently as the solution to a global optimisation problem. Solving the models with prioritised branching and valid inequalities in Gurobi, we can compute the frustration index of real signed networks with over 15000 edges in less than a minute on inexpensive hardware. We provide extensive performance analysis for both random and real signed networks and show that our models outperform all existing approaches by large factors. Based on solve time, algorithm output, and effective branching factor we highlight the superiority of our models to both exact and heuristic methods in the literature.
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