Partitioning a square into rectangles: NP-Completeness and approximation algorithms

Algorithmica (New York)

Volumn 34, Issue 3, 2002, Pages 217-239

  Beaumont, Olivier ^a   Boudet, Vincent ^a   Rastello, Fabrice ^a   Robert, Yves ^a  

^a UNIVERSITÉ DE LYON   (France)

Author keywords

Approximation algorithms; Geometric problems; Heterogeneous resources; Np completeness; Parallel computing

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; PARALLEL ALGORITHMS;

HETEROGENEOUS RESOURCES;

PARALLEL PROCESSING SYSTEMS;

EID: 0141922734     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-002-0962-9     Document Type: Article

References (13)

1. N. Alon and D.J. Kleitman. Covering a square by small perimeter rectangles. Discrete Compat. Geom., 1:1-7, 1986.
2. G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation. Springer-Verlag, Berlin, 1999.
3. O. Beaumont, V. Boudet, F. Rastello, and Y. Robert. Matrix multiplication on heterogeneous platforms. IEEE Trans. Parallel Distrib. Systems, 12(10): 1033-1051, 2001.
4. L.S. Blackford, J. Choi, A. Cleary, E. D'Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R.C. Whaley. ScaLAPACK Users' Guide. SIAM, Philadelphia, PA, 1997.
5. ̃viggo/wwwcompendium/wwwcompendium.html.
6. M.R. Garey and D.S. Johnson. Computers and Intractability, a Guide to the Theory of NP-Completeness. Freeman, San Francisco, CA, 1991.
7. T.F. Gonzalez and S. Zheng. Improved bounds for rectangular and guillotine partitions. J. Symbolic Comput., 7:591-610, 1989.
8. T.F. Gonzalez and S. Zheng. Approximation algorithm for partitioning a rectangle with interior points. Algorithmica, 5:11-42, 1990.
9. S. Khanna, S. Muthukrishnan, and M. Paterson. On approximating rectangle tiling and packing. In Proc. 9th Ann. ACM-SIAM Symposium on Discrete Algorithms, pages 384-393. ACM Press, New York, 1998.
10. S. Khanna, S. Muthukrishnan, and S. Skiena. Efficient array partitioning. In Proc. 24th Internal. Colloquium on Automata, Languages and Programming, LNCS 1256, pages 616-626. Springer-Verlag, Berlin, 1997.
11. T.Y. Kong, D.M. Mount, and W. Roscoe. The decomposition of a rectangle into rectangles of minimal perimeter. SIAM J. Comput., 17(6):1215-1231, 1988.
12. T.Y. Kong, D.M. Mount, and M. Wermann. The decomposition of a square into rectangles of minimal perimeter. Discrete Appl. Math., 16:239-243, 1987.
13. A. Lingas, R.Y. Pinter, R.L. Rivest, and A. Shamir. Minimum edge length partitioning of rectilinear polygons. In Proc. 20th Ann. Allerton Conference on Communication, Control and Computing, pages 53-63, 1982.