Approximation algorithms for geometric tour and network design problems

Proceedings of the Annual Symposium on Computational Geometry

Volumn Part F129372, Issue , 1995, Pages 360-369

  Mata, Cristian S ^a   Mitchell, Joseph S B ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85017742265     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/220279.220318     Document Type: Conference Paper

References (26)

1. P. K. Agarwal and S. Suri. Surface approximation and geometric partitions. In Proc. Fifth Annual ACM-SIAMSympos. on Discrete Algorithms, 1994, pages 34-43.
2. E. M. Arkin and R. Hassin. Approximation algorithms for the geometric covering salesman problem. Discrete Applied Math, 55:197-218, 1994.
3. E. M. Arkin, S. Khuller, and J. S. B. Mitchell. Geometric knapsack problems. Algorithmica, 10:399-427, 1993.
4. B. Awerbuch, Y. Azar, A. Blum, and S. Vempala. Improved approximation guarantees for minimum-weight A:-trees and prize-collecting salesmen. To appear, STOC 1995.
5. M. de Berg and M. van Kreveld. Rectilinear decompositions with low stabbing number. Tech. Report RUU-CS-93-25, Dept. Comput. Sci., Utrecht Univ., 1993.
6. A. Blum, P. Chalasani, and S. Vempala. A constant-factor approximation for the A:-MST problem in the plane. To appear, STOC 1995.
7. S. Carlsson, H. Jonsson, and B. J. Nilsson. Finding the shortest watchman route in a simple polygon. In Proc. 4th Annu. Internat. Sympos. Algorithms Comput. (ISAAC 93), LNCS Vol. 762, pp. 58-67, Springer-Verlag, 1993.
8. W. Chin and S. Ntafos. Optimum watchman routes. Inform. Process. Lett., 28:39-44, 1988.
9. N. Christofides. Worst-case analysis of a new heuristic for the traveling salesman problem. In J. F. Traub, editor, Sympos. on New Directions and Recent Results in Algorithms and Complexity, New York, NY, 1976. Academic Press.
10. K. L. Clarkson. Approximation algorithms for planar traveling salesman tours and minimum-length triangulations. In Proc. Second Annual ACM-SIAM Sympos. on Discrete Algorithms, 1991, pages 17-23.
11. D.-Z. Du, L.-Q. Pan, and M.-T. Shing. Minimum edge length guillotine rectangular partition. Report 02418-86, Math. Sci. Res. Inst., Univ. California, Berkeley, CA, 1986.
12. P. Eades and D. Rappaport. The complexity of computing minimum separating polygons. Pattern Recognition Letters, 14:715-718, 1993.
13. D. Eppstein. Approximating the minimum weight triangula-tion. In Proc. Third Annual ACM-SIAM Sympos. Discrete Algorithms, 1992, pages 48-57.
14. S. Fekete. On the complexity of min-link red-blue separation. Manuscript, 1992.
15. N. Garg and D. S. Hochbaum. An O (log k) approximation algorithm for the k minimum spanning tree problem in the plane. In Proc. 26th Annu. ACM Sympos. Theory Comput. (STOC 94), pages 432-438, 1994.
16. T. Gonzalez, M. Razzazi, and S.-Q. Zheng. An efficient divide-and-conquer approximation algorithm for hyperrectangular partitions. In Proc. 2nd Canad. Conf. Comput. Geom., pages 214-217, 1990.
17. J. Hershberger and S. Suri. A pedestrian approach to ray shooting: Shoot a ray, take a walk. In Proc. 4 th ACM-SIAM Sympos. Discrete Algorithms, pages 54-63, 1993.
18. E. Ihler, G. Reich, and P. Widmayer. On shortest networks for classes of points in the plane. In Computational Geometry - Methods, Algorithms and Applications: Proc. Internat. Workshop Comput. Geom. CG'91, LNCS Vol. 553, pp. 103-111. Springer-Verlag, 1991.
19. C. Levcopoulos. Fast heuristics for minimum length rectangular partitions of polygons. In Proc. 2nd Annu. ACM Sympos. Comput. Geom., pages 100-108, 1986.
20. C. Levcopoulos. Heuristics for minimum decompositions of polygons. PhD diss. No. 155, Linkoping University 1987.
21. C. Levcopoulos and A. Lingas. Bounds on the length of convex partitions of polygons. In Proc. 4th Conf. Found. Softw. Tech. Theoret. Comput. Sci., LNCS Vol. 181, pp. 279-295. Springer-Verlag, 1984.
22. J. S. B. Mitchell. Approximation algorithms for geometric separation problems. Technical report, AMS Dept., SUNY Stony Brook, NY, July 1993.
23. B. J. Nilsson. Guarding art galleries - Methods for mobile guards. Ph. D. thesis, Lund University, 1995.
24. M. S. Paterson and F. F. Yao. Efficient binary space partitions for hidden-surface removal and solid modeling. Discrete Comput. Geom., 5:485-503, 1990.
25. M. S. Paterson and F. F. Yao. Optimal binary space partitions for orthogonal objects. J. Algorithms, 13:99-113, 1992.
26. G. Reich and P. Widmayer. Beyond Steiner's problem: A VLSI oriented generalization. In Proc. 15th Internat. Workshop Graph-Theoret. Concepts Comput. Sci., LNCS Vol. 411, pp. 196-210. Springer-Verlag, 1989.