Exact Methods for the Vertex Bisection Problem

Fraire, Héctor; Terán-Villanueva, J. David; Castillo-García, Norberto; Barbosa, Juan Javier González; Angel, Eduardo Rodríguez del; Rojas, Yazmin

doi:10.1007/978-3-319-05170-3_40

Cited by 10 publications

(9 citation statements)

References 3 publications

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“…If x i = 0, then v ij = 0 using constraint (2). If x i =1 and x j = 0, then from using constraints (2) and (3) v ij may be 0 or 1 but constraint (4) guarantees that v ij = 1 not 0. If x i =1 and x j = 1, v ij = 0 using constraint (3).…”

Section: Ilp Formulationmentioning

confidence: 99%

“…Brandes and Fleisher [1] proved that Vertex Bisection minimization problem is NP-complete in general but vertex bisection minimization is polynomially solvable for trees and hypercubes. Fraire et al [4] have proposed two ILP models and one QCQP for VBMP. In this paper, we have proposed a 0-1 ILP model and two QCQP models which requires fewer number of variables and constraints than the one proposed by [4].…”

Section: Introductionmentioning

confidence: 99%

“…Fraire et al [4] have proposed two ILP models and one QCQP for VBMP. In this paper, we have proposed a 0-1 ILP model and two QCQP models which requires fewer number of variables and constraints than the one proposed by [4].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Jain¹,

Saran²,

Srivastava³

2016

JAMRIS

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Section: Ilp Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Jain¹,

Saran²,

Srivastava³

2016

JAMRIS

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“…El VBP ha sido resuelto en la literatura por métodos estocásticos y exactos. Los más recientes y relevantes métodos exactos para resolverlo son dos algoritmos de ramificación y acotamiento en [6] y en [8]. En [6], proponen un algoritmo exhaustivo.…”

Section: Introductionunclassified

“…Los más recientes y relevantes métodos exactos para resolverlo son dos algoritmos de ramificación y acotamiento en [6] y en [8]. En [6], proponen un algoritmo exhaustivo. En su experimentación, usan un benchmark compuesto de 108 instancias: 5 Grids, 84 Small, 15 Trees y 4 Harwell-Boeing.…”

Section: Introductionunclassified

Un nuevo algoritmo de ramificación y acotamiento para el problema de la bisección de vértices

Ángel-Martínez¹,

Fraire-Huacuja²,

Soto³

et al. 2019

RCS

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In this paper we approach the exact solution of the vertex bisection problem. It is a NP-hard problem which ocurrs in the context of 331 communication networks. Currently, the best state-of-the-arte algorithm is the BBVBMP, it use the branch-and-bound methodology. In this paper, we propose a new algorithm based in the same methodology. Our proposal takes advantage of a constructive heuristic to initiliaize the upper bound. This heuristic considers the degree of the vertex candidates. Also, the proposed algorithm explores the search tree in the combinatorial space with a maximum height of n/2 nodes, decreasing the size of the tree. The performance of the new heuristics was measure with a benchmark set with known optimals by construction. The experimental results shows that the heuristic in the porposed algorithm outperforms in eficiency the heuristic incorporated in BBVBMP. Finally, the performace of the proposed algorithm is compared against the BBVBMP when solving the vertex bisection problem benchmark. The results show that the proposed algorithm reach the same quality solution as BBVBMP, with a reduction in the execution time of 15 %.

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