An exact method for computing the frustration index in signed networks using binary programming

28 Nov 2016  ·  Samin Aref, Andrew J. Mason, Mark C. Wilson ·

Computing the frustration index of a signed graph is a key step toward solving problems in many fields including social networks, physics, material science, 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 1960, 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.

PDF Abstract

Categories


Social and Information Networks Optimization and Control 90C10, 90C20, 90C35, 90C57, 90C90, 05C15, 11E16, 65K05

Datasets


  Add Datasets introduced or used in this paper