On the optimality of planar and geometric approximation schemes

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2007, Pages 338-348

  Marx, Dániel ^a,b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SCIENCE; FIBER OPTIC CHEMICAL SENSORS; FOUNDATIONS; GEOMETRY; POLYNOMIAL APPROXIMATION;

APPROXIMATION SCHEMES; GEOMETRIC APPROXIMATIONS; GEOMETRIC PROBLEMS; OPTIMALITY;

COMPUTATIONAL GEOMETRY;

EID: 46749156309     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2007.4389505     Document Type: Conference Paper

References (28)

1. P. K. Agarwal, M. van Kreveld, and S. Suri. Label placement by maximum independent set in rectangles. Comput. Geom., 11(3-4):209-218, 1998.
2. J. Alber, H. Fernau, and R. Niedermeier. Parameterized complexity: exponential speed-up for planar graph problems. J. Algorithms, 52(1):26-56, 2004.
3. J. Alber and J. Fiala. Geometric separation and exact solutions for the parameterized independent set problem on disk graphs. J. Algorithms, 52(2): 134-151, 2004.
4. A. Andoni, P. Indyk, and M. Patrascu. On the optimality of the dimensionality reduction method. In FOCS '06: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06), pages 449-458, Washington, DC, USA, 2006. IEEE Computer Society.
5. S. Arora. Polynomial time approximation schemes for Euclidean TSP and other geometric problems. In FOCS 1996, pages 2-11. IEEE Comput. Soc. Press, 1996.
6. S. Arora. Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. J. ACM, 45(5):753-782, 1998.
7. B. S. Baker. Approximation algorithms for NP-complete problems on planar graphs. J. ACM, 41(1):153-180, 1994.
8. C. Bazgan. Schémas d'approximation et complexité paramétrée. Technical report, Université Paris Sud, 1995.
9. L. Cai, M. Fellows, D. Juedes, and F. Rosamond. The complexity of polynomial-time approximation, 2006. To appear in Theory of Computing Systems.
10. M. Cesati and L. Trevisan. On the efficiency of polynomial time approximation schemes. Inform. Process. Lett., 64(4):165-171, 1997.
11. J. Chen, X. Huang, I. A. Kanj, and G. Xia. Linear FPT reductions and computational lower bounds. In STOC 2004, pages 212-221, New York, 2004. ACM.
12. I. Dinur. The PCP theorem by gap amplification. In STOC 2006, pages 241-250, 2006.
13. R. G. Downey. Parameterized complexity for the skeptic. In Proceedings of the 18th IEEE Annual Conference on Computational Complexity, pages 147-169, 2003.
14. M. Grigni, E. Koutsoupias, and C. Papadimitriou. An approximation scheme for planar graph TSP. In FOCS 1995, pages 640-645. IEEE, Los Alamitos, CA, 1995.
15. H. B. Hunt, III, M. V. Marathe, V. Radhakrishnan, S. S. Ravi, D. J. Rosenkrantz, and R. E. Stearns. NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs. J. Algorithms, 26(2):238-274, 1998.
16. R. Impagliazzo, R. Paturi, and F. Zane. Which problems have strongly exponential complexity? J. Comput. System Sci., 63(4):512-530, 2001.
17. S. Khanna and R. Motwani. Towards a syntactic characterization of PTAS. In STOC 1996, pages 329-337.
18. S. Khanna, M. Sudan, L. Trevisan, and D. P. Williamson. The approximability of constraint satisfaction problems. SIAM J. Comput., 30(6):1863-1920, 2001.
19. P. Klein. A linear-time approximation scheme for planar weighted TSP. In FOCS 2005, pages 647-656. IEEE, 2005.
20. R. J. Lipton and R. E. Tarjan. A separator theorem for planar graphs. SIAM J. Appl. Math., 36(2):177-189, 1979.
21. R. J. Lipton and R. E. Tarjan. Applications of a planar separator theorem. SIAM J. Comput., 9(3):615-627, 1980.
22. E. Malesińska. Graph-Theoretical Models for Frequency Assignment Problems. PhD thesis, TU Berlin, 1997.
23. D. Marx. The closest substring problem with small distances. In FOCS 2005, pages 63-72, 2005.
24. D. Marx. Efficient approximation schemes for geometric problems? In ESA 2005, pages 448-459, 2005.
25. D. Marx. Parameterized complexity and approximation algorithms, 2006. To appear in The Computer Journal.
26. S. B. Rao and W. D. Smith. Approximating geometrical graphs via "spanners" and "banyans". In STOC '98 (Dallas, TX), pages 540-550. ACM, New York, 1999.
27. E. J. van Leeuwen. Better approximation schemes for disk graphs. In SWAT 2006, pages 316-327, 2006.
28. D. W. Wang and Y-S. Kuo. A study on two geometric location problems. Inform. Process. Lett., 28(6):281-286, 1988.