# A Comparison of Several Bandwidth and Profile Reduction Algorithms

@article{Gibbs1976ACO, title={A Comparison of Several Bandwidth and Profile Reduction Algorithms}, author={N. Gibbs and William G. Poole and P. Stockmeyer}, journal={ACM Trans. Math. Softw.}, year={1976}, volume={2}, pages={322-330} }

Abstract : This paper compares and analyzes six algorithms which have been suggested recently for use in reducing, by permutations, the bandwidth and profile of sparse matrices. This problem arises in many different areas of scientific computation such as in the finite element method for approximating solutions of partial differential equations and in analyzing large-scale power transmission systems.

#### 110 Citations

Algorithm 508: Matrix Bandwidth and Profile Reduction [F1]

- Computer Science
- TOMS
- 1976

This program was extensively tested and compared with several other programs and was found to be considerably faster than the others, generally superior for bandwidth reduction and as satisfactory as any other for profile reduction. Expand

Heuristic Spectral Techniques for the Reduction of Bandwidth and Work-Bound of Sparse Matrices

- Mathematics, Computer Science
- Numerical Algorithms
- 2004

These algorithms are inspired by the spectral method of Barnard, Pothen and Simon (1995), which derives a permutation for reducing the envelope-size of a sparse matrix by computing the second eigenvector of the associated Laplacian matrix. Expand

Discrete Optimization Heuristics for matrix bandwidth reduction

- Computer Science
- 2006

Experiments show these heuristics improve solution quality when compared with the well-known GPS algorithm and recently-developed methods using tabu search and GRASP with Path Relinking. Expand

Heuristics for matrix bandwidth reduction

- Mathematics, Computer Science
- Eur. J. Oper. Res.
- 2006

Experiments show these heuristics improve solution quality when compared with the well-known GPS algorithm and recently-developed methods using tabu search and GRASP with Path Relinking. Expand

A hybrid algorithm for reducing matrix bandwidth

- Mathematics
- 1984

A hybrid algorithm for reducing the bandwidth of symmetric matrices is described in terms of a finite element grid. The new algorithm produces significantly lower bandwidths than either the… Expand

Algorithm 509: A Hybrid Profile Reduction Algorithm [F1]

- Computer Science
- TOMS
- 1976

A new "hybrid" algorithm for reducing profile is presented which combines the better features of [3] and [5] by first finding a pseudodiameter to produce a leveling and then numbering the leveling level by level according to King's criteria. Expand

An algorithm for profile and wavefront reduction of sparse matrices

- Mathematics
- 1986

SUMMARY An algorithm for reducing the profile and wavefront of a sparse matrix is described. The scheme is applicable to any sparse matrix which has a symmetric pattern of zeros and may be used to… Expand

A comparison of algorithms for profile reduction of sparse matrices

- Mathematics
- 1995

A comparison is undertaken of a number of algorithms for profile reduction of sparse symmetric banded positive definite matrices based on results reported in the literature, with regard to the… Expand

Reducing the bandwidth of a sparse matrix with tabu search

- Mathematics, Computer Science
- Eur. J. Oper. Res.
- 2001

This work designs and test a special type of candidate list strategy and a move mechanism to be embedded in a tabu search procedure for the bandwidth reduction problem and shows that the proposed procedure outperforms the best-known algorithms in terms of solution quality consuming a reasonable computational effort. Expand

A systematic review of heuristics for symmetric-matrix bandwidth reduction : methods not based on metaheuristics

- 2015

Heuristics for bandwidth reduction of matrices is used to reduce computational and storage costs of resolution of large sparse linear systems. Bandwidth reduction consists of carrying out… Expand

#### References

SHOWING 1-10 OF 14 REFERENCES

An algorithm for reducing the bandwidth and profile of a sparse matrix

- Mathematics
- 1976

A new algorithm for reducing the bandwidth and profile of a sparse matrix is described. Extensive testing on finite element matrices indicates that the algorithm typically produces bandwidth and… Expand

Several Strategies for Reducing the Bandwidth of Matrices

- Computer Science
- 1972

This work uses the finite element displacement method for analyzing a wide variety of structures, and the need for automating the data generation for such analyses, to find the solution of systems of linear equations involving sparse, symmetric, positive definite coefficient matrices. Expand

Reducing the bandwidth of sparse symmetric matrices

- Computer Science, Mathematics
- ACM '69
- 1969

A direct method of obtaining an automatic nodal numbering scheme to ensure that the corresponding coefficient matrix will have a narrow bandwidth is presented. Expand

An automatic reordering scheme for simultaneous equations derived from network systems

- Computer Science
- 1970

Comparative Analysis of the Cuthill–McKee and the Reverse Cuthill–McKee Ordering Algorithms for Sparse Matrices

- Mathematics
- 1976

In this paper we examine the Cuthill–McKee algorithm for ordering the unknowns and equations in systems of linear equations, $A{\bf x} = {\bf b}$, where A is sparse, symmetric, and positive definite.… Expand

Computer implementation of the finite element method

- Mathematics
- 1971

Abstract : A detailed study of the implementation of finite element methods for solving two-dimensional elliptic partial differential equations is presented. Generation and storage schemes for… Expand

Recent improvements to BANDIT

- Computer Science
- 1975

It is shown that, compared to the Cuthill-McKee algorithm on which BANDIT was originally based, GPS is faster and achieves similar results. Expand

An empirical investigation of reordering and data management for finite element systems of equations. Rep. ANL8056

- 1973

ACM Transactions on Mathematical Software

- ACM Transactions on Mathematical Software
- 1976

C Recent improvements to BANDIT

- 1975