Octants Are Cover-Decomposable

1. B. Ács, Síkfedések szétbonthatósága. Master Thesis (in Hungarian). http://www.cs.elte.hu/blobs/diplomamunkak/mat/2010/acs_bernadett.pdf

2. Aloupis, G., Cardinal, J., Collette, S., Langerman, S., Orden, D., Ramos, P.: Decomposition of multiple coverings into more parts. In: SODA, pp. 302–310 (2009)

   Google Scholar 

3. Buchsbaum, A.L., Efrat, A., Jain, S., Venkatasubramanian, S., Yi, K.: Restricted strip covering and the sensor cover problem. In: SODA, pp. 1056–1063 (2007)

   Google Scholar 

4. Cardinal, J.: personal communication

5. Gibson, M., Varadarajan, K.: Decomposing coverings and the planar sensor cover problem. arXiv:0905.1093v1

6. Keszegh, B.: Weak conflict-free colorings of point sets and simple regions. In: The 19th Canadian Conference on Computational Geometry (CCCG07), Proceedings, pp. 97–100 (2007)

   Google Scholar 

7. Cardinal, J., Korman, M.: Coloring planar homothets and three-dimensional hypergraphs. arXiv:1101.0565

8. König, D.: Theorie der Endlichen und Unendlichen Graphen, Kombinatorische Topologie der Streckenkomplexe. Akademie Verlag, Leipzig

9. Pach, J.: Decomposition of multiple packing and covering. In: 2. Kolloq. Diskrete Geometrie, Salzburg, pp. 169–178. Math. Inst. Univ. Salzburg, Salzburg (1980)

   Google Scholar 

10. Pach, J.: Covering the plane with convex polygons. Discrete Comput. Geom. 1, 73–81 (1986)

    Article  MathSciNet  MATH  Google Scholar 

11. Pach, J., Pálvölgyi, D., Tóth, G.: Survey on the decomposition of multiple coverings. To appear

12. Pach, J., Tardos, G., Tóth, G.: Indecomposable coverings. Can. Math. Bull. 52, 451–463 (2009)

    Article  MATH  Google Scholar 

13. Pach, J., Tóth, G.: Decomposition of multiple coverings into many parts. In: 23rd ACM Symposium on Computational Geometry, pp. 133–137. ACM Press, New York (2007). Also in: Discrete Comput. Geom. 42, 127–133 (2009)

    Google Scholar 

14. Pálvölgyi, D.: Decomposition of geometric set systems and graphs. Ph.D. thesis. arXiv:1009.4641

15. Pálvölgyi, D.: Indecomposable coverings with concave polygons. Discrete Comput. Geom. 44(3), 577–588 (2010)

    Article  MathSciNet  MATH  Google Scholar 

16. Pálvölgyi, D., Tóth, G.: Convex polygons are cover-decomposable. Discrete Comput. Geom. 43(3), 483–496 (2010)

    Article  MathSciNet  MATH  Google Scholar 

17. Tardos, G., Tóth, G.: Multiple coverings of the plane with triangles. Discrete Comput. Geom. 38, 443–450 (2007)

    Article  MathSciNet  MATH  Google Scholar 

18. Varadarajan, K.: Weighted geometric set cover via quasi-uniform sampling. In: STOC, pp. 641–648 (2010)

    Google Scholar 

Download references