Complexities of Efficient Solutions of Rectilinear Polygon Cover Problems

Algorithmica (New York)

Volumn 17, Issue 4, 1997, Pages 331-356

  Berman, P ^a   DasGupta, B ^b  

^a The Pennsylvania State University   (United States)

^b University of Minnesota   (United States)

Author keywords

Approximation schemes; Cover; Heuristics; Polygon; Rectangle; Rectilinear

Indexed keywords

EID: 0006727665     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02523677     Document Type: Article

References (21)

1. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof Verification and Hardness of Approximation Problems. Proc. 33rd IEEE Symp. on Foundations of Computer Science (FOCS), 1992, pp. 14-23.
2. P. Berman and B. DasGupta. Results on Approximation of the Rectilinear Polygon Cover Problems. Tech. Rep. # CS-92-06, Pennsylvania State University, June, 1992.
3. P. Berman and G. Schnitger. On the Complexity of Approximating the Independent Set Problem. Inform. and Comput., 96 (1992), 77-94.
4. S. Chaiken, D. J. Kleitman, M. Saks, and J. Shearer. Covering Regions by Rectangles. SIAM J. Algebraic Discrete Methods, 2 (1981), 394-410.
5. H. E. Conn and J. O'Rourke. Some Restricted Rectangle Covering Problems. Tech Rep. JHU-87/13, Johns Hopkins University, Baltimore, MD, 1987. Also appeared in Proc. Allerton Conference, 1987. pp. 898-907.
6. H. E. Conn and J. O'Rourke. Some Restricted Rectangle Covering Problems. Tech Rep. JHU-87/13, Johns Hopkins University, Baltimore, MD, 1987. Also appeared in Proc. Allerton Conference, 1987. pp. 898-907.
7. T. H. Corman, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, MA, 1990.
8. J. C. Culberson and R. A. Reckhow. Covering Polygon Is Hard. J. Algorithms, 17 (1994), 2-44.
9. D. S. Franzblau. Performance Guarantees on a Sweep-Line Heuristic for Covering Rectilinear Polygons with Rectangles. SIAM J. Discrete Math., 2 (1989), 307-321.
10. D. S. Franzblau and D. J. Kleitman. An Algorithm for Covering Polygons with Rectangles. Inform. and Control, 63(3) (1984), 164-189.
11. M. R. Garey and D. S. Johnson. Computers and Intractability - A Guide to the Theory of NP-Completeness. Freeman, San Francisco, CA, 1979.
12. 5/2 Algorithm for Maximum Matching in Bipartite Graphs. SIAM J. Comput., 2 (1979), 225-231.
13. A. Lubiw. Ordering and Some Combinatorial Optimization Problems with Some Geometric Applications. Ph.D. Thesis, University of Waterloo, Ontario, 1985.
14. A. Lubiw. The Boolean Basis Problem and How to Cover Polygons by Rectangles. Manuscript, University of Waterloo, Ontario, 1988. Referenced in [8].
15. W. J. Masek. Some NP-Complete Set Covering Problems. Unpublished manuscript, MIT, Cambridge, MA. Referenced in [10].
16. C. Mead and L. Conway. Introduction to VLSI Systems. Addison-Wesley, Reading, MA, 1980, Chapters 2 and 4.
17. R. Motwani, A. Raghunathan, and H. Saran. Perfect Graphs and Orthogonally Convex Covers. SIAM J. Discrete Math., 2 (1989), 371-392.
18. T. Ohtsuki. Minimum Dissection of Rectilinear Polygons. Proc. IEEE Symp. on Circuits and Systems, 1982, pp. 1210-1213.
19. J. O'Rourke and K. J. Supowit. Some HP-Hard Polygon Decomposition Problems. IEEE Trans. Inform. Theory, 29 (1983), 181-190.
20. L. Pagli, E. Lodi, F. Luccio, C. Mugnai, and W. Lipski. On Two-Dimensional Data Organization 2. Fund. Inform., 2 (1979), 211-226.
21. C. H. Papadimitriou and M. Yannakakis. Optimization, Approximation and Complexity Classes. J. Computer System Sci., 43 (1991), 425-440.