Conflict-free colorings of simple geometric regions with applications to frequency assignment in cellular networks

SIAM Journal on Computing

Volumn 33, Issue 1, 2003, Pages 94-136

  Even, Guy ^a   Lotker, Zvi ^a   Ron, Dana ^a   Smorodinsky, Shakhar ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Approximation algorithms; Computational geometry; Conflict free coloring; Frequency assignment

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CELLULAR RADIO SYSTEMS; CLIENT SERVER COMPUTER SYSTEMS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; CONSTRAINT THEORY; FREQUENCY ALLOCATION; MATHEMATICAL MODELS; RADIO LINKS; SET THEORY; THEOREM PROVING;

APPROXIMATION ALGORITHMS; CELLULAR NETWORKS; CONFLICT FREE COLORINGS; FREQUENCY ASSIGNMENT;

GRAPH THEORY;

EID: 1842459431     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539702431840     Document Type: Article

References (20)

1. K. Aardal, S. van Hoesel, A. Koster, C. Mannino, and A. Sassano, Models and Solutions Techniques for Frequency Assignment Problem, ZIB Report 01-40, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Berlin, Germany, 2001; available online at http://www.zib.de/PaperWeb/abstracts/ZR-01-40/.
2. Z. Abrams, J. Könemann, A. Meyerzson, K. Munagala, and S. Plotkin, Facility Location with Interference, Working paper 2001-E23, GSTA, Carnegie Mellon University, Pittsburgh, PA, 2001.
3. K. Appel and W. Haken, Every planar map is 4-colorable-1: Discharging, Illinois J. Math., 21 (1977), pp. 421-490.
4. K. Appel and W. Haken, Every planar map is 4-colorable-2: Reducibility, Illinois J. Math., 21 (1977), pp. 491-567.
5. R. Bar-Yehuda, O. Goldreich, and A. Itai, On the time-complexity of broadcast in multi-hop radio networks: An exponential gap between determinism and randomization, J. Comput. System Sci., 45 (1992), pp. 104-126.
6. R. Bar-Yehuda, personal communication, Technion, Israel Institute of Technology, Haifa, Israel, 2001.
7. M. De Berg, M. Van Kreveld, M. Overmars, and O. Schwartzkopf, Computational Geometry - Algorithms and Applications, Springer-Verlag, Berlin, New York, 1997.
8. B. N. Clark, C. J. Colburn, and D. S. Johnson, Unit disks graphs, Discrete Math., 86 (1990), pp. 165-177.
9. H. S. M. Coxeter, Introduction to Geometry, 2nd ed., Wiley, New York, 1969.
10. N. W. Dunkin, J. E. Bater, P. G. Jeavons, and D. A. Cohen, Towards High Order Constraint Representations for the Frequency Assignment Problem, Technical report CSD-TR-98-05, Computer Science Department, Royal Holloway, University of London, London, 1998; available online at http://www.dcs.rhbnc.ac.uk/research/constraints/publications/index.shtml.
11. U. Feige and J. Kilian, Zero knowledge and the chromatic number, J. Comput. System Sci., 57 (1998), pp. 187-199.
12. M. Galota, C. Glasser, S. Reith, and H. Vollmer, A Polynomial-Time Approximation Scheme for Base Station Positioning in UMTS Networks, Technical report 264, Institut für Informatik, Universität Würzburg, Würzburg, Germany, 2000.
13. S. Har-Peled and S. Smorodinsky, On conflict-free coloring of points and simple regions in the plane, in Proceedings of the 19th Annual ACM Symposium on Computing Geometry, San Diego, CA, 2003, pp. 114-123.
14. X. Huang, Automatic Cell Planning for Mobile Network Design: Optimization Models and Algorithms, Ph.D. dissertation, Universität Karlsruhe, Karlsruhe, Germany, 2001.
15. S. O. Krumke, M. V. Marathe, and S. S. Ravi, Models and approximation algorithms for channel assignment in radio networks, invited paper in Wireless Networks, 7 (2001), pp. 575-584.
16. M. V. Marathe, H. Breu, H. B. Hunt, III, S. S. Ravi, and D. J. Rosenkrantz, Simple heuristics for unit disk graphs, Networks, 25 (1995), pp. 59-68.
17. J. Pach and G. Tóth, Conflict free colorings, in The Goodman Pollack Festschrift, Algorithms Combin. 25, B. Aronov, S. Basu, J. Pach, and M. Sharir, eds., Springer-Verlag, Berlin, 2003, pp. 665-671.
18. M. Sharir and P. Agarwal, Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge University Press, Cambridge, UK, 1995.
19. S. Smorodinsky, Combinatorial Problems in Computational Geometry, Ph.D dissertation, Tel-Aviv University, Tel-Aviv, Israel, 2003.
20. R. Robertson, D. P. Sanders, P. Seymour, and R. Thomas, Efficiently four-coloring planar graphs, in Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, Philadelphia, PA, 1996, pp. 571-575.