# Object-oriented algorithmic laboratory for ordering sparse matrices

## Abstract

We focus on two known NP-hard problems that have applications in sparse matrix computations: the envelope/wavefront reduction problem and the fill reduction problem. Envelope/wavefront reducing orderings have a wide range of applications including profile and frontal solvers, incomplete factorization preconditioning, graph reordering for cache performance, gene sequencing, and spatial databases. Fill reducing orderings are generally limited to--but an inextricable part of--sparse matrix factorization. Our major contribution to this field is the design of new and improved heuristics for these NP-hard problems and their efficient implementation in a robust, cross-platform, object-oriented software package. In this body of research, we (1) examine current ordering algorithms, analyze their asymptotic complexity, and characterize their behavior in model problems, (2) introduce new and improved algorithms that address deficiencies found in previous heuristics, (3) implement an object-oriented library of these algorithms in a robust, modular fashion without significant loss of efficiency, and (4) extend our algorithms and software to address both generalized and constrained problems. We stress that the major contribution is the algorithms and the implementation; the whole being greater than the sum of its parts. The initial motivation for implementing our algorithms in object-oriented software was to manage the inherent complexity. During our researchmore »

- Authors:

- Univ. of California, Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 15013116

- Report Number(s):
- UCRL-LR-136934

TRN: US200604%%120

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Thesis/Dissertation

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 59 BASIC BIOLOGICAL SCIENCES; 97 MATHEMATICS AND COMPUTING; ALGORITHMS; DESIGN; EFFICIENCY; FACTORIZATION; GENES; IMPLEMENTATION; MATRICES; PERFORMANCE

### Citation Formats

```
Kumfert, Gary Karl.
```*Object-oriented algorithmic laboratory for ordering sparse matrices*. United States: N. p., 2000.
Web. doi:10.2172/15013116.

```
Kumfert, Gary Karl.
```*Object-oriented algorithmic laboratory for ordering sparse matrices*. United States. doi:10.2172/15013116.

```
Kumfert, Gary Karl. Mon .
"Object-oriented algorithmic laboratory for ordering sparse matrices". United States. doi:10.2172/15013116. https://www.osti.gov/servlets/purl/15013116.
```

```
@article{osti_15013116,
```

title = {Object-oriented algorithmic laboratory for ordering sparse matrices},

author = {Kumfert, Gary Karl},

abstractNote = {We focus on two known NP-hard problems that have applications in sparse matrix computations: the envelope/wavefront reduction problem and the fill reduction problem. Envelope/wavefront reducing orderings have a wide range of applications including profile and frontal solvers, incomplete factorization preconditioning, graph reordering for cache performance, gene sequencing, and spatial databases. Fill reducing orderings are generally limited to--but an inextricable part of--sparse matrix factorization. Our major contribution to this field is the design of new and improved heuristics for these NP-hard problems and their efficient implementation in a robust, cross-platform, object-oriented software package. In this body of research, we (1) examine current ordering algorithms, analyze their asymptotic complexity, and characterize their behavior in model problems, (2) introduce new and improved algorithms that address deficiencies found in previous heuristics, (3) implement an object-oriented library of these algorithms in a robust, modular fashion without significant loss of efficiency, and (4) extend our algorithms and software to address both generalized and constrained problems. We stress that the major contribution is the algorithms and the implementation; the whole being greater than the sum of its parts. The initial motivation for implementing our algorithms in object-oriented software was to manage the inherent complexity. During our research came the realization that the object-oriented implementation enabled new possibilities augmented algorithms that would not have been as natural to generalize from a procedural implementation. Some extensions are constructed from a family of related algorithmic components, thereby creating a poly-algorithm that can adapt its strategy to the properties of the specific problem instance dynamically. Other algorithms are tailored for special constraints by aggregating algorithmic components and having them collaboratively generate the global ordering. Our software laboratory, ''Spinole'', implements state-of-the-art ordering algorithms for sparse matrices and graphs. We have used it to examine and augment the behavior of existing algorithms and test new ones. Its 40,000+ lilies of C++ code includes a base library test drivers, sample applications, and interfaces to C, C++, Matlab, and PETSc. Spinole is freely available and can be built on a variety of UNIX platforms as well as WindowsNT.},

doi = {10.2172/15013116},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2000},

month = {5}

}