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Matrix Decomposition by Branch-and-Cut

Please always quote using this URN: urn:nbn:de:0297-zib-2839
  • In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called {\em bordered block diagonal form}. More precisely, given some matrix $A$, we try to assign as many rows as possible to some number of blocks of limited size such that no two rows assigned 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 %LP- and MIP-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.

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Author:Ralf BorndörferORCiD, Carlos E. Ferreira, Alexander Martin
Document Type:ZIB-Report
Date of first Publication:1997/03/17
Series (Serial Number):ZIB-Report (SC-97-14)
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