Two models of two-dimensional bandwidth problems

Lin, Lan; Yao, Lin

doi:10.1016/j.ipl.2010.04.013

Cited by 6 publications

(4 citation statements)

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“…Some generalizations of MBMP are currently investigated by the world researchers. For example, the twodimensional bandwidth problem is to embed a graph into a planar grid such that the maximum distance between adjacent vertices is as small as possible [14].…”

Section: Matrix Bandwidth Minimization Problem Descriptionmentioning

confidence: 99%

Soft Computing Approaches on the Bandwidth Problem

et al. 2013

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The Matrix Bandwidth Minimization Problem (MBMP ) seeks for a simultaneous reordering of the rows and the columns of a square matrix such that the nonzero entries are collected within a band of small width close to the main diagonal. The MBMP is a NP-complete problem, with applications in many scientific domains, linear systems, artificial intelligence, and real-life situations in industry, logistics, information recovery. The complex problems are hard to solve, that is why any attempt to improve their solutions is beneficent. Genetic algorithms and ant-based systems are Soft Computing methods used in this paper in order to solve some MBMP instances. Our approach is based on a learning agent-based model involving a local search procedure. The algorithm is compared with the classical Cuthill-McKee algorithm, and with a hybrid genetic algorithm, using several instances from Matrix Market collection. Computational experiments confirm a good performance of the proposed algorithms for the considered set of MBMP instances. On Soft Computing basis, we also propose a new theoretical Reinforcement Learning model for solving the MBMP problem.

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Section: Matrix Bandwidth Minimization Problem Descriptionmentioning

confidence: 99%

Soft Computing Approaches on the Bandwidth Problem

et al. 2013

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“…This distance does not mean the length of wire connecting points (i, j) and (i , j ), but it is meaningful in representing dilation in some interconnection network architectures (see, e.g., [12]). Based on this type of distance in the plane, we have another model of two-dimensional bandwidth problem [9]: the bandwidth of labelling f for G is…”

Section: Preliminariesmentioning

confidence: 99%

“…where D(G) is the diameter of G. For two-dimensional bandwidth, the density lower bound and the corresponding upper bound are as follows (obtained in [5,9]).…”

Section: Preliminariesmentioning

confidence: 99%

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Square-root rule of two-dimensional bandwidth problem

Lin

Yao

2011

RAIRO-Theor. Inf. Appl.

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The bandwidth minimization problem is of significance in network communication and related areas. Let G be a graph of n vertices. The two-dimensional bandwidth B2(G) of G is the minimum value of the maximum distance between adjacent vertices when G is embedded into an n × n grid in the plane. As a discrete optimization problem, determining B2(G) is NP-hard in general. However, exact results for this parameter can be derived for some special classes of graphs. This paper studies the "square-root rule" of the twodimensional bandwidth, which is useful in evaluating B2(G) for some typical graphs.

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