Decomposing Matrices into Blocks

Borndörfer R, E. Ferreira C, Martin A (1998)

Publication Language: English

Publication Type: Journal article

Publication year: 1998

Journal

SIAM Journal on Optimization Society for Industrial and Applied Mathematics

Publisher: Society for Industrial and Applied Mathematics

Book Volume: 9

Pages Range: 236 -- 269

Abstract

In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called bordered block diagonal form. More precisely, given some matrix A, we try to assign as many rows as possible to some number β of blocks of size script K such that no two rows as signed to different blocks intersect in a common column. Bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems. We show that various matrices from the linear programming and mixed integer programming libraries Netlib and Miplib can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality. These computations are done with a branch-and-cut algorithm based on polyhedral investigations of the matrix decomposition problem. In practice, however, one would use heuristics to find a good decomposition. We present several heuristic ideas and test their performance. Finally, we investigate the usefulness of optimal matrix decompositions into bordered block diagonal form for integer programming by using such decompositions to guide the branching process in a branch-and-cut code for general mixed integer programs.

Authors with CRIS profile

Alexander Martin Economics - Discrete Optimization - Mathematics (EDOM)

Involved external institutions

University of São Paulo / Universidade de São Paulo (USP) BR Brazil (BR) Konrad-Zuse-Zentrum für Informationstechnik / Zuse Institute Berlin (ZIB) DE Germany (DE)

How to cite

APA:

Borndörfer, R., E. Ferreira, C., & Martin, A. (1998). Decomposing Matrices into Blocks. SIAM Journal on Optimization, 9, 236 -- 269.

MLA:

Borndörfer, Ralf, Carlos E. Ferreira, and Alexander Martin. "Decomposing Matrices into Blocks." SIAM Journal on Optimization 9 (1998): 236 -- 269.

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