A new Integer Linear Programming and Quadratically Constrained Quadratic Programming Formulation for Vertex Bisection Minimization Problem
TLDR
A new integer linear programming (ILP) and quadratically constrained quadratic programming (QCQP) formulation for VBMP is proposed and implemented and optimal results for various classes of graphs are obtained.Abstract:
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.read more
Citations
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Journal ArticleDOI
A variable neighborhood search approach for the vertex bisection problem
TL;DR: This paper uses Basic Variable Neighborhood Search (BVNS) methodology to solve the Vertex Bisection Problem and introduces a novel scheme for calculating the objective function which substantially reduces the computing time as compared with the direct implementation.
Journal ArticleDOI
On minimizing vertex bisection using a memetic algorithm
TL;DR: A memetic algorithm has been designed for this problem (MAVBMP) in which four construction heuristics have been proposed to generate the initial population and a new crossover type search operator has been proposed for recombination and a local improvement operator has also been developed.
Journal ArticleDOI
Two efficient local search algorithms for the vertex bisection minimization problem
TL;DR: In this article , the authors developed two efficient local search algorithms for vertex bisection minimization problem (VBMP), namely, BVNSbucket and BVnsbucket2 .
Journal ArticleDOI
Two new integer linear programming formulations for the vertex bisection problem
TL;DR: Two new integer linear programming (ILP) formulations for VBP are proposed and the experimental results clearly indicate that these formulations outperform ILPLIT in average objective value, average computing time and number of optimal solutions found.
References
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Improved Approximation Algorithms for MAX k-CUT and MAX BISECTION
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Variable neighborhood search for the Vertex Separation Problem
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