TY - GEN
A1 - BorndÃ¶rfer, Ralf
A1 - Ferreira, Carlos E.
A1 - Martin, Alexander
T1 - Decomposing Matrices into Blocks
N2 - 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 MITLIB 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.
T3 - ZIB-Report - SC-97-15
Y1 - 1997
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/284
UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-2849
ER -