Decomposing matrices into blocks

SIAM Journal on Optimization

Volumn 9, Issue 1, 1998, Pages 236-269

  Borndörfer, Ralf ^a   Ferreira, Carlos E ^b   Martin, Alexander ^a  

^a ZUSE INSTITUTE BERLIN   (Germany)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Block structure of a sparse matrix; Cutting planes; Integer programming; Matrix decomposition; Polyhedral combinatorics

Indexed keywords

EID: 0040631469     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623497318682     Document Type: Article

References (28)

1. R. E. BIXBY, private communication.
2. C. C. CARØE AND R. SCHULTZ, Dual Decomposition in Stochastic Integer Programming, Preprint SC 96-46, Konrad Zuse Zentrum für Informationstechnik Berlin, 1996; also available online from http://www.zib.de/ZIBbib/Publications; Oper. Res. Lett., submitted.
3. Y. CRAMA AND M. OOSTEN, Models for machine-part grouping in cellular manufacturing, Internat. J. Prod. Res., 34 (1996), pp. 1693-1713.
4. D. DENTCHEVA, R. GOLLMER, A. MÖLLER, W. RÖMISCH, AND R. SCHULTZ, Solving the unit commitment problem in power generation by primal and dual methods, in Proc. 9th Conf. of the European Consortium for Math. in Industry (ECMI), Copenhagen, 1996, M. Bendsøe and M. Sørensen, eds., Teubner Verlag, Stuttgart, 1997.
5. I. DUFF, A. ERISMAN, AND J. REID, Direct Methods for Sparse Matrices, Oxford Univ. Press, Oxford, UK, 1986.
6. M. EHRGOTT, Optimierungsprobleme in Graphen unter Kardinalitätsrestriktionen, Master's thesis, Dept. of Mathematics, Univ. Kaiserslautern, Kaiserslautern, Germany, 1992.
7. C. E. FERREIRA, A. MARTIN, C. C. DE SOUZA, R. WEISMANTEL, AND L. A. WOLSEY, The node capacitated graph partitioning problem: A computational study, Math. Programming, 81 (1998), pp. 229-256.
8. C. E. FERREIRA, A. MARTIN, AND R. WEISMANTEL, Solving multiple knapsack problems by cutting planes, SIAM J. Optim., 6 (1996), pp. 858-877.
9. C. FlDUCCIA AND R. MATTHEYSES, A linear-time heuristic for improving network partitions, Proc. 19th IEEE Design Automation Conference, Las Vegas, NV, 1982, pp. 175-181.
10. A. GALLIVAN, M. T. HEATH, E. NG, J. M. ORTEGA, B. W. PEYTON, R. J. PLEMMONS, C. H. ROMINE, A. H. SAMEH, AND R. G. VOIGT, Parallel Algorithms for Matrix Computations, SIAM, Philadelphia, 1990.
11. M. R. GAREY AND D. S. JOHNSON, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, New York, 1979.
12. E. GOTTLIEB AND M. RAO, The generalized assignment problem: Valid inequalities and facets, Math. Programming, 46 (1990), pp. 31-52.
13. M. GRÖTSCHEL, L. LOVÁSZ, AND A. SCHRIJVER, Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, Berlin, 1988.
14. M. GRÖTSCHEL, A. MARTIN, AND R. WEISMANTEL, Packing Steiner trees: A cutting plane algorithm and computational results, Math. Programming, 72 (1996), pp. 125-145.
15. A. GUPTA, Fast and Effective Algorithms for Graph Partitioning and Sparse Matrix Ordering, Tech. report RC 20496, IBM T. J. Watson Res. Center, Yorktown Heights, NY, 1996.
16. C. HELMBERG, B. MOHAR, S. POLJAK, AND F. RENDL, A spectral approach to bandwidth and separator problems in graphs, Linear and Multilinear Algebra, 39 (1995), pp. 73-90.
17. K. L. HOFFMAN AND M. W. PADBERG, Solving airline crew-scheduling problems by branchand-cut, Mgmt. Sci., 39 (1993), pp. 657-682.
18. ILOG CPLEX DIVISION, Using the CPLEX Callable Library, Incline Village, NV, 1997. Information available online from http://www.cplex.com.
19. V. KUMAR, A. GRAMA, A. GUPTA, AND G. KARYPIS, Introduction to Parallel Computing, Benjamin-Cummings, Menlo Park, CA, 1994.
20. T. LENGAUER, Combinatorial Algorithms for Integrated Circuit Layout, B.G. Teubner, Stuttgart, and John Wiley & Sons, Chichester, 1990.
21. A. LÖBEL, Optimal Vehicle Scheduling in Public Transit, Shaker Verlag, Aachen, 1998.
22. S. NICOLOSO AND P. NOBILI, A set covering formulation of the matrix equipartition problem, in System Modelling and Optimization, Proc. 15th IFIP Conf., Zürich, Sept. 1991, P. Kall, ed., Springer-Verlag, Berlin, Heidelberg, New York, 1992, pp. 189-198.
23. P. NOBILI AND A. SASSANO, Facets and lifting procedures for the set covering polytope, Math. Programming, 45 (1989), pp. 111-137.
24. M. W. PADBERG, On the facial structure of set packing polyhedra, Math. Programming, 5 (1973), pp. 199-215.
25. A. POTHEN, H. D. SIMON, AND K.-P. LIOU, Partitioning sparse matrices with eigenvectors of graphs, SIAM J. Matrix Anal., 11 (1990), pp. 430-452.
26. E. ROTHBERG AND B. HENDRICKSON, Sparse Matrix Ordering Methods for Interior Point Linear Programming, Tech. report SAND96-0475J, Sandia National Laboratories, Albuquerque, NM, 1996.
27. A. SCHRIJVER, Theory of Linear and Integer Programming, John Wiley and Sons, Chichester, 1986.
28. G. SHEBLE AND G. FAHD, Unit commitment literature synopsis, IEEE Trans. Power Systems, 9 (1994), pp. 128-135.