Optimal Rectangular Partitions

Networks

Volumn 41, Issue 1, 2003, Pages 51-67

  Calheiros, Felipe C ^a   Lucena, Abilio ^b   De Souza, Cid C ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Cutting planes; Lagrangian relaxation; Optimality properties; Rectangular partitions

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; INTEGER PROGRAMMING; LINEAR PROGRAMMING; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

CUTTING PLANES; LANGRAGIAN RELAXATION; OPTIMALITY PROPERTIES; RECTANGULAR PARTITIONS;

COMPUTATIONAL GEOMETRY;

EID: 2142775466     PISSN: 00283045     EISSN: None     Source Type: Journal    
DOI: 10.1002/net.10058     Document Type: Article

References (20)

1. CPLEX ILOG, Inc. CPLEX Division, 1999.
2. C.N. de Meneses and C.C. de Souza, Exact solutions of optimal rectangular partitions via integer programming, Int J Comput Geom Appl 10 (2000), 477-522.
3. M. de Moraes Palmeira, A. Lucena, and O. Porto, A relax and cut algorithm for quadratic knapsack problem, Technical report, Laboratório de Métodos Quantitatives, Departamento de Administração, Universidade Federal do Rio de Janeiro, 1999.
4. D.Z. Du, L.Q. Pan, and M.T. Shing, Minimum edge length guillotine rectangular partition, Technical report MSRI 02418-86, Mathematical Sciences Research Institute, Berkeley, CA, 1986.
5. L. Escudero, M. Guignard, and K. Malik, A Lagrangian relax and cut approach for the sequential ordering problem with precedence constraints, Ann Oper Res 50 (1994), 219-237.
6. M.L. Fisher, The Lagrangian relaxation method for solving integer programming problems, Mgmt Sci 27 (1981), 1-18.
7. T.F. Gonzalez, M. Razzazi, M.T. Shing, and S.Q. Zheng, On optimal guillotine partitions approximating optimal d-box partitions, Comput Geom 4 (1994), 1-11.
8. T.F. Gonzalez, M. Razzazi, and S.Q. Zheng, An efficient divide-and-conquer approximation algorithm for partitioning into d-boxes, Int J Comput Geom Appl 3 (1993), 281-287.
9. T.F. Gonzalez and S.Q. Zheng, Bounds for partitioning rectilinear polygons, Proc 1st Ann Symp on Computational Geometry, ACM, Baltimore, MD, 1985, pp. 281-287.
10. T.F. Gonzalez and S.Q. Zheng, Improved bounds for rectangular and guillotine partitions, J Symb Comput 7 (1989), 591-610.
11. T.F. Gonzalez and S.Q. Zheng, Approximation algorithms for partitioning a rectangle with interior points, Algorithmica 5 (1990), 11-42.
12. M. Held, P. Wolfe, and H.P. Crowder, Validation of subgradient optimization, Math Program 6 (1974), 62-88.
13. M. Hunting, U. Faigle, and W. Kern, A Lagrangian relaxation approach to the edge-weighted clique problem, Eur J Oper Res 131 (2001), 119-131.
14. C. Levcopoulos, Fast heuristics for minimum length rectangular partitions of polygons, Proc 2nd Ann Symp on Computational Geometry, ACM, Yorktown Heights, NY, 1986, pp. 100-108.
15. A. Lingas, R.Y. Pinter, R.L. Rivest, and A. Shamir, Minimum edge length partitioning of rectlinear polygons, Proc 20th Ann Allerton Conf on Communication, Control and Computing, University of Illinois Press, Monticello, IL, 1982, pp. 53-63.
16. A. Lucena, Steiner problem in graphs: Lagrangian relaxation and cutting-planes, COAL Bull 21 (1982), 2-8.
17. A. Lucena, Tight bounds for the Steiner problem in graphs, Proc NETFLOW93, Technical report TR-21/93, Universitá degli Studi di Pisa, Dipartimento di Informatica, Pisa, Italy, 1993, pp. 147-154.
18. C. Martinhon, A. Lucena, and N. Maculan, A relax and cut algorithm for the vehicle routing problem, Technical report, Laboratório de Métodos Quantitatives, Departamento de Administração, Universidade Federal do Rio de Janeiro, 2000.
19. J.S.B. Mitchell, Guillotine subdivisions approximate polygonal subdivisions: Part II - A simple polynomial-time approximation scheme for geometric k-MST, TSF, and related problems, SIAM J Comput 28 (1999), 1298-1309.
20. G.L. Nemhauser and G. Sigismondi, A strong cutting plane branch-and-bound algorithm for node packing, J Oper Res Soc 43 (1992), 443-457.