Branch and Bound Algorithm for Vertex Bisection Minimization Problem

Jain, Pallavi; Saran, Gur; Srivastava, Kamal

doi:10.1007/978-981-10-1023-1_2

Cited by 7 publications

(9 citation statements)

References 7 publications

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“…Nuestra propuesta es una heurística constructiva voraz para generar un límite superior inicial para el VBP. En esta sección se describen dos heurísticas: la primera heurística (H1) es de [8]; la segunda heurística (H2) genera un conjunto se soluciones que le permiten seleccionar la que presenta un mejor valor objetivo.…”

Section: Definición De La Cota Superiorunclassified

“…Mientras el número de elementos en B sea inferior a n/2 , se selecciona un elemento de B en el cual su número de vecinos que no forman parte de B y que no sea 0, es mínimo, agregándolo a B junto con el conjunto de sus vecinos que no forman parte de B, o un subconjunto del mismo si no es posible agregarlos en su totalidad. (Para más detalles vea [8]).…”

Section: Cota Superior Con H1unclassified

“…Nuestra propuesta utiliza la mejor heurística de la experimentación anterior. La segunda prueba es una réplica de la experimentación reportada en [8].…”

Section: Experimentos Computacionalesunclassified

“…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

“…En su experimentación, usan un benchmark compuesto de 108 instancias: 5 Grids, 84 Small, 15 Trees y 4 Harwell-Boeing. En [8], proponen un algoritmo de ramificación y acotamiento llamado BBVBMP, el cual utiliza una heurística constructiva para generar una cota superior inicial. Además, proponen un nuevo cálculo de la cota inferior.…”

Section: Introductionunclassified

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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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Section: Definición De La Cota Superiorunclassified

Section: Cota Superior Con H1unclassified

“…Nuestra propuesta utiliza la mejor heurística de la experimentación anterior. La segunda prueba es una réplica de la experimentación reportada en [8].…”

Section: Experimentos Computacionalesunclassified

Section: Introductionunclassified

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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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Two new integer linear programming formulations for the vertex bisection problem

Castillo-García

Hernández

2019

Comput Optim Appl

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The vertex bisection problem (VBP) is an NP-hard combinatorial optimization problem with important practical applications in the context of network communications. The problem consists in finding a partition of the set of vertices of a generic undirected graph into two subsets (A and B) of approximately the same cardinality in such a way that the number of vertices in A with at least one adjacent vertex in B is minimized. In this article, we propose two new integer linear programming (ILP) formulations for VBP. Our first formulation (ILPVBP) is based on the redefinition of the objective function of VBP. The redefinition consists in computing the objective value from the vertices in B rather than from the vertices in A. As far as we are aware, this is the first time that this representation is used to solve VBP. The second formulation (MILP) reformulates ILPVBP in such a way that the number of variables and constraints is reduced. In order to assess the performance of our formulations, we conducted a computational experiment and compare the results with the best ILP formulation available in the literature (ILPLIT). The experimental results clearly indicate that our formulations outperform ILPLIT in (i) average objective value, (ii) average computing time and (iii) number of optimal solutions found. We statistically validate the results of the experiment through the well-known Wilcoxon rank sum test for a confidence level of 99.9%. Additionally, we provide 404 new optimal solutions and 73 new upper and lower bounds for 477 instances from 13 different groups of graphs.

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Two efficient local search algorithms for the vertex bisection minimization problem

Tian

Ouyang²,

Sun³

et al. 2022

Information Sciences

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Branch and Bound Algorithm for Vertex Bisection Minimization Problem

Cited by 7 publications

References 7 publications

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

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

Two new integer linear programming formulations for the vertex bisection problem

Two efficient local search algorithms for the vertex bisection minimization problem

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