Finding Exact Solutions to the Bandwidth Minimization Problem

Corso, Gianna M. Del; Manzini, Giovanni

doi:10.1007/s006070050002

Cited by 33 publications

(31 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Caprara and Salazar (2004) also introduce the following three integer linear programming problems to obtain lower bounds on B g (G) that we denote as ILP 1 (g,u i ), ILP 2 (g) and ILP 3 (g) 1 . They state that the maximum value of ILP 1 (g,u i ) for i=1,.., k is equal to LB 1 (g), the value of ILP 2 (g) gives the lower bound proposed by Del Corso and Manzini (1999), and ILP 3 (g) provides a tighter lower bound of B g (G) than the other two problems. u∈A,v∈F,(u,v…”

Section: Previous Theoretical Resultsmentioning

confidence: 99%

“…The codes were compiled with Microsoft Visual C++ 6.0, optimizing for maximum speed. Caprara and Salazar (2004) show that their two methods, LeftToRight and Both, outperform the procedures introduced by Del Corso and Manzini (1999). We therefore compare our method with these two methods identified as the best.…”

Section: Computational Experimentsmentioning

confidence: 91%

“…Del Corso and Manzini (1999) propose two exact branch and bound methods. The first algorithm (MB_ID) uses a depth first search strategy, while the second one (MB_PS) extends it with the perimeter strategy to improve the search performance.…”

Section: Previous Branch and Bound Algorithmsmentioning

confidence: 99%

See 2 more Smart Citations

A branch and bound algorithm for the matrix bandwidth minimization

Martı́

Campos

Piñana

2008

European Journal of Operational Research

View full text Add to dashboard Cite

-In this article we first review previous exact approaches as well as theoretical contributions for the problem of reducing the bandwidth of a matrix. This problem consists of finding a permutation of the rows and columns of a given matrix which keeps the non-zero elements in a band that is as close as possible to the main diagonal. This NP-complete problem can also be formulated as a labeling of vertices on a graph, where edges are the non-zero elements of the corresponding symmetrical matrix. We propose a new branch and bound algorithm and new expressions for known lower bounds for this problem.Empirical results with a collection of previously reported instances indicate that the proposed algorithm compares favourably to previous methods.

show abstract

Section: Previous Theoretical Resultsmentioning

confidence: 99%

Section: Computational Experimentsmentioning

confidence: 91%

See 1 more Smart Citation

A branch and bound algorithm for the matrix bandwidth minimization

Martı́

Campos

Piñana

2008

European Journal of Operational Research

View full text Add to dashboard Cite

show abstract

“…While the envelope is only indirectly related to the bandwidth of a matrix, this algorithm is very effective at reducing it. Further information on these and other classic methods for the BMP can be found in [7,20].…”

Section: Introductionmentioning

confidence: 99%

A Hyper-Heuristic Approach to Evolving Algorithms for Bandwidth Reduction Based on Genetic Programming

Koohestani

Poli

2011

Research and Development in Intelligent Systems XXVIII

View full text Add to dashboard Cite

The bandwidth reduction problem is a well-known NP-complete graphlayout problem that consists of labeling the vertices of a graph with integer labels in such a way as to minimize the maximum absolute difference between the labels of adjacent vertices. The problem is isomorphic to the important problem of reordering the rows and columns of a symmetric matrix so that its non-zero entries are maximally close to the main diagonal -a problem which presents itself in a large number of domains in science and engineering. A considerable number of methods have been developed to reduce the bandwidth, among which graph-theoretic approaches are typically faster and more effective. In this paper, a hyper-heuristic approach based on genetic programming is presented for evolving graph-theoretic bandwidth reduction algorithms. The algorithms generated from our hyper-heuristic are extremely effective. We test the best of such evolved algorithms on a large set of standard benchmarks from the Harwell-Boeing sparse matrix collection against two state-of-the-art algorithms from the literature. Our algorithm outperforms both algorithms by a significant margin, clearly indicating the promise of the approach.

show abstract

Section: Introductionmentioning

confidence: 99%

A Genetic Programming Approach to the Matrix Bandwidth-Minimization Problem

Koohestani

Poli

2010

Parallel Problem Solving From Nature, PPSN XI

View full text Add to dashboard Cite

Abstract. The bandwidth of a sparse matrix is the distance from the main diagonal beyond which all elements of the matrix are zero. The bandwidth minimisation problem for a matrix consists of finding the permutation of rows and columns of the matrix which ensures that the non-zero elements are located in as narrow a band as possible along the main diagonal. This problem, which is known to be NP-complete, can also be formulated as a vertex labelling problem for a graph whose edges represent the non-zero elements of the matrix. In this paper, a Genetic Programming approach is proposed and tested against two of the best-known and widely used bandwidth reduction algorithms. Results have been extremely encouraging.Keywords: Bandwidth Minimization Problem; Genetic Programming; Graph Labelling; Sparse Matrices; Combinatorial Optimisation. BackgroundThe Bandwidth Minimization Problem (BMP) is a very well-known problem, familiar to applied mathematicians and arising in many applications in science and engineering [18]. BMP consists of finding the permutation of rows and columns of a matrix which ensures that the non-zero elements are located in as narrow a band as possible along the main diagonal. One of the most common applications of bandwidth-minimisation algorithms arises from the need to efficiently solve large systems of equations [19]. In such a scenario, more efficient solutions are obtained if the rows and columns of the matrix representing the set of equations can be permuted in such a way that the bandwidth of the matrix is minimized [19]. BMP has also connections with a wide range of other problems, including: finite element analysis of mechanical systems, large scale power transmission systems, circuit design, VLSI design, data storage, chemical kinetics, network survivability, numerical geophysics, industrial electromagnetics, saving large hypertext media and topology compression of road networks.The BMP is NP-complete [18] and, hence, it is highly unlikely that there exists an algorithm which finds the minimum bandwidth of a matrix in polynomial time. It has also been proved that the BMP is NP-complete even for trees with

show abstract

Finding Exact Solutions to the Bandwidth Minimization Problem

Cited by 33 publications

References 17 publications

A branch and bound algorithm for the matrix bandwidth minimization

A branch and bound algorithm for the matrix bandwidth minimization

A Hyper-Heuristic Approach to Evolving Algorithms for Bandwidth Reduction Based on Genetic Programming

A Genetic Programming Approach to the Matrix Bandwidth-Minimization Problem

Contact Info

Product

Resources

About