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A new Integer Linear Programming and Quadratically Constrained Quadratic Programming Formulation for Vertex Bisection Minimization Problem

Vertex Bisection Minimization problem (VBMP) consists of partitioning a vertex set V of graph G = (V, E) into two sets B and B′ where ∣B∣ = such that vertex width (VW) is minimized where vertex width is defined as the number of vertices in B which are adjacent to at least one vertex in B′. It is an NP-complete problem in general. VBMP has applications in fault tolerance and is related to the complexity of sending messages to processors in interconnection networks via vertex disjoint paths. In this paper, we have proposed a new integer linear programming (ILP) and quadratically constrained quadratic programming (QCQP) formulation for VBMP. Both of them require number of variables and constraints lesser than existing ILPs and QCQP. We have also implemented ILP and obtained optimal results for various classes of graphs. The result of the experiments with the benchmark graphs shows that the proposed model outperforms the state of the art. Moreover, proposed model obtains optimal result for all the benchmark graphs.