Exact Methods for the Vertex Bisection Problem
In this chapter we approach the vertex bisection problem (VB), which is relevant in the context of communication networks. A literature review shows that the reported exact methods are restricted to solve particular graph cases. As a first step to solve the problem for general graphs using soft computing techniques, we propose two new integer-linear programming models and a new branch and bound algorithm (B&B). For the first time, the optimal solutions for an extensive set of standard instances were obtained.
The authors thank Consejo Nacional de Ciencia y Tecnología (CONACYT), Dirección General de Educación Superior Tecnológica (DGEST) and Instituto Tecnológico de Ciudad Madero (ITCM) for their financial support to this project. Also we thank to IBM Academic Initiative for the software support (CPLEX 12.5).