Maintenance of a piercing set for intervals with applications

Algorithmica (New York)

Volumn 36, Issue 1, 2003, Pages 59-73

  Katz, Matthew J ^a   Nielsen, Frank ^b   Segal, Michael ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b SONY COMPUTER SCIENCE LABORATORIES INC   (Japan)

Author keywords

Dynamic algorithms; Geometric optimization; Piercing set

Indexed keywords

APPROXIMATION THEORY; DATA STRUCTURES; GRAPH THEORY; OPTIMIZATION; PROBLEM SOLVING; THEOREM PROVING; TREES (MATHEMATICS);

DYNAMIC ALGORITHMS; GEOMETRIC OPTIMIZATION; PIERCING SET; SHOOTER LOCATION PROBLEM;

SET THEORY;

EID: 0942279290     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-002-1006-1     Document Type: Article

References (16)

1. J. Chaudhuri and S. C. Nandy, Generalized shooter location problem, in T. Asano, H. Imai, D. T. Lee, S. Nakano, and T. Tokuyama (eds.), 5th Annual International Conference, COCOON'99, Tokyo, Japan, July 1999. Proceedings, Lecture Notes in Computer Science 1627, pp. 389-399, Springer-Verlag, Berlin, 1999.
2. B. Chazelle, Cutting hyperplanes for divide-and-conquer, Discrete Comput. Geom., 9 (1993), 145-158.
3. K. Daniels and V. Milenkoyic, Limited gaps, in Proc. 6th Canad. Conf. Comput. Geom., pp. 225-231, 1994.
4. R. J. Fowler, M. S. Paterson, and S. L. Tanimoto, Optimal packing and covering in the plane are NP-complete, Inform. Process. Lett., 12(3) (1981), 133-137.
5. M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
6. M. C. Golumbic and P. L. Hammer, Stability in circular arc graphs, J. Algorithms, 9 (1988), 314-320.
7. U. Gupta, D. T. Lee and Y.-T. Leung, Efficient algorithms for interval graphs and circular-arc graphs. Networks, 12 (1982), 459-467.
8. W.-L. Hsu and K.-H. Tsai, Linear time algorithms on circular-arc graphs, Inform. Process. Lett., 40 (1991), 123-129.
9. D. T. Lee, M. Sarafzadeh, and Y. F. Wu, Minimum cuts for circular-arc graphs, SIAM J. Comput., 19(6) (1990), 1041-1050.
10. S. Masuda and K. Nakajima, An optimal algorithm for finding a maximum independent set of a circular-arc graphs, SIAM J. Comput., 17(1) (1988), 41-52.
11. S. C. Nandy, K. Mukphopadhyaya, and B. B. Bhattacharya, Shooter location problem, in Proc. 8th Canad. Conf. Comput. Geom., pp. 93-98, 1996.
12. F. Nielsen, Fast stabbing of boxes in high dimensions, Theoret. Comput. Sci., 246 (2000), 53-72.
13. A. S. Rao and C. P. Rangan, Optimal parallel algorithms on circular-arc graphs, Inform. Process. Lett., 33 (1989), 147-156.
14. R. E. Tarjan, Data Structures and Network Algorithms, Regional Conference Series in Applied Mathematics 44, SIAM, Philadephia, PA, 1983.
15. K. H. Tsai and D. T. Lee, k-Best cuts for circular-arc graphs, Algorithmica, 18(2) (1997), 198-216.
16. C. A. Wang and B. Zhu, Shooter location problems revisited, in Proc. 9th Canad. Conf. Comput. Geom., pp. 223-228, 1997.