An improved nodal ordering for reducing the bandwidth in fem. Us patent for softwaredefined memory bandwidth reduction. Similarly, the upper bandwidth is the smallest number p such that a i,j 0 whenever i matrix has lower bandwidth. I have a sparse symmetric matrix of dimension 93x93 8308 no zero elements, with bandwidth 80. Chira, a hybrid aco approach to the matrix bandwidth minimization problem, m. Since 1969 a standard approach to the reduction of matrix bandwidth and profile has been to grow rooted level structures rlss of the adjacency graph of the matrix, and then to use the best rls to.
Adaptive memory programming for matrix bandwidth minimization, annals of operations research, springer, vol. Algorithms for the reduction of matrix bandwidth and profile. B bandwidth a,type returns the bandwidth of matrix a specified by type. The program was coded in the c language and the parallelism was supported by openmp. I was solving a problem which involved finding the bandwidth of a matrix. Matrix bandwidth and profile reduction, acm transactions on mathematical software, volume 2, number 4, december 1976. I interpreted the bandwidth as a nonnegative number which is closest to the diagonal. You can make it equal to be 1 by swapping a 3, 1 and a 3, 3, i. Since 1969 a standard approach to the reduction of matrix bandwidth and profile has been to grow rooted level structures rlss of the adjacency graph.
Raltr2005001 reducing the total bandwidth of a sparse unsymmetric matrix1. A constructive bandwidth reduction algorithma variant of. An optimized leveled parallel rcm for bandwidth reduction. Although it supports symmetric matrices by storing only the upper or lower triangle, the multiplication algorithm requires streaming the triangular matrix twice. Siam journal on numerical analysis siam society for. You can not make swaps in any way that can reduce the bandwidth of this matrix. A constructive bandwidth reduction algorithma variant of gps. A disadvantage is that choosing a higher bandwidth results in a reduction. Department of civil and structural engineering, the university, mappin street, sheffield s1 3jd, united kingdom.
Reducing the bandwidth of a sparse matrix with tabu search. The bandwidth reduction problem consists of finding a labeling f that minimizes bf g. The same sequence with a bandwidth of 300 will give you the option to reduce the minimum tr to 450 and te to 16 reducing the scan time from 3. An investigation of algorithms for matrix bandwidth. When gaussian elimination with row interchanges is applied, the lower bandwidth is unaltered while the upper bandwidth.
Of the gibbs poolestockmeyer algorithm i flfflflfflflc. A reduction in the bandwidth allows to attenuate the. An evaluation of lowcost heuristics for matrix bandwidth. Although the fnchc and vnsband heuristics obtained the best results in relation to bandwidth reduction in the sets composed of 18 and 45 asymmetric instances of the harwellboeing sparse matrix. An important special type of sparse matrices is band matrix, defined as follows. We begin in section 2 by commenting on the importance of reordering a matrix to block form prior to applying a bandwidth reduction. The following is a comparison of jcl and gps on the examples in algorithms for reducing the bandwidth and profile of a sparse matrix. Specify type as lower for the lower bandwidth, or upper for the upper bandwidth. In terms of profile reduction snays 1969 algorithm resulted in better profile than rcm.
Heuristics for bandwidth reduction of matrices is used to reduce computational and storage costs of resolution of large sparse linear systems. Reducing the total bandwidth of a sparse unsymmetric matrix stfc. Bandwidth reduction, finite element method, sparse symmetric matrix. Bandwidth and wavefront are well studied metrics used in sparse matrix solvers. The paper describes a new bandwidth reduction method for sparse matrices which promises to be both fast and effective in comparison with known methods. The problem of reordering a sparse symmetric matrix in reducing the bandwidth, has played a central role in the solution of sparse linear systems. With this approach, the bandwidth is reduced in more than 50% of instances of benchmark tests compared with the outcomes of the existing algorithms. If we call this matrix b, then im interested in calculate the inverse irhob, where i is a diagonal matrix and rho is a parameter updated in my mcmc algorithm. There is a direct correspondence between the structure of the coefficient matrix, called the stiffness matrix in this case, and the structure of the spatial network delineating the element layout. A hybrid profile reduction algorithm, acm transactions on mathematical software, volume 2, number 4, december 1976, pages 378387. For the efficient solution of these systems of equations, it is desirable to have an automatic nodal numbering or renumbering scheme to ensure that the corresponding coefficient matrix will have a narrow bandwidth. This tutorial shows how the bandwidth of the nonzero pattern of a sparse matrix can be reduced by renumbering the unknowns i. The bandit computer program for the reduction of matrix bandwidth for nastran.
A new algorithm for reducing the bandwidth and profile of a sparse matrix is. Smyth unit for computer science, mcmaster university, hamilton, ontario, canada abstract. Many algorithms for reducing the bandwidth of a sparse symmetric matrix a. Heuristics for matrix bandwidth reduction citeseerx. The 50% reduction in memory bandwidth does not readily translate to a 2x improvement, possibly because the number of cache misses due to vector accesses is increased due.
Pdf bandwidth reduction in sparse matrices researchgate. Extensive testing on finite element matrices indicates that the algorithm typically produces bandwidth and profile which. The report describes a matrix bandwidth reduction preprocessor for use with the nasa structural analysis computer program, nastran. Bandwidth of this matrix is equal to 1, which is the minimum bandwidth that you can get. Gps bandwidth and profile reduction of sparse matrix. Asfaraswe cansee, little hasbeendonefortheunsymmetricmatrixa, whichhas distinct lower and upper bandwidths l and u. Reducing the total bandwidth of a sparse unsymmetric matrix. Note that a labeling is simply a renumbering of the vertices. One of the earliest software packages to implement bandwidth and profile reduction, called reduce crane. Matrix bandwidth reduction is therefore critical for solving large sparse linear systems. A lot of algorithms have been proposed for the problem of matrix bandwidth or pro. The problem of reordering a sparse symmetric matrix to reduce the bandwidth has. Bandit computer program for the reduction of matrix bandwidth for nastran, nsrdc report 3827, march 1972. In this work we prove that span is limited by twice the bandwidth of a matrix.
Software defined memory bandwidth reduction by hierarchical stream buffering for general matrix multiplication in a programmable ic oct 17, 2017 xilinx, inc. Many bandwidth reduction algorithms have been developed since the 1960s and. In numerical linear algebra, the cuthillmckee algorithm cm, named for elizabeth cuthill and james mckee, is an algorithm to permute a sparse matrix that has a symmetric sparsity pattern into a band matrix form with a small bandwidth. Martin, an algorithm for reducing the bandwidth of a matrix of symmetrical configuration. In this work, a heuristic for bandwidth and profile reductions of symmetric and asymmetric matrices using a onedimensional selforganizing map is proposed. An algorithm for reducing the bandwidth and profile of a. Another algorithm for reducing bandwidth and profile of a. Reducing the bandwidth of sparse symmetric matrices. If we let a aij be the incidence matrix of a graph v i. Of the three algorithms, the collins approach appears most appealing because of its simplicity and good performance in reducing bandwidths. A computer program, bandit, is described which was developed for use as a preprocessor to nastran to automatically resequence the grid point numbers for reduced matrix bandwidth.
Interchange opportunity in average bandwidth reduction in. Heuristics for matrix bandwidth reduction request pdf. Transactions on mathematical software 2 4 1976 322330. A new heuristic for bandwidth and profile reductions of. By cuthillmckee algorithm, i could achieve a new matrix with bandwidth 89. Experiments and comparisons of results obtained were performed in relation to results of the variable neighborhood search for bandwidth reduction. In this paper, a new viable bandwidth reduction algorithm for reducing the bandwidth of sparse symmetric matrices, is described. While the above cited algorithms have made important contributions to the study of bandwidth reduction, they are restricted to the case in which the sparse matrix.
Norman gibbs, william poole, paul stockmeyer, an algorithm for reducing the bandwidth and profile of a sparse matrix. Bandwidth reduction, profile reduction, wavefront reduction, sparise matrix, banded matrix, matrix reordering. Simulation results show that with the proposed algorithm, sometimes bandwidth and pro. A new mode renumbering algorithm for bandwidth reduction.
I wrote solving beacause the problem is after all npcomplete and none of the algorithms described claimed to find the exact solutions regardless of the input matrix. Parallel implementations of rcm algorithm for bandwidth reduction. Back in the 60s and 70s many graph algorithms were proposed for solving the bandwidth reduction problem. Matrix bandwidth and profile reduction, acm transactions on mathematical software, volume 2, number 4, december 1976, pages 375377. Methods and apparatus are described for partitioning and reordering blockbased matrix multiplications for highspeed data streaming in general matrix. Scott abstract for a sparse symmetric matrix, there has been much attention given to algorithms for reducing. The reverse cuthillmckee algorithm rcm due to alan george is the same algorithm but with the resulting index numbers reversed. Interchange opportunity in average bandwidth reduction in sparse matrices. For a sparse symmetric matrix, there has been much attention given to algorithms for reducing thebandwidth.
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