Abstract
In this paper we describe together with an overview about other results the main ideas of our polynomial time approximation schemes for the maximum weight independent set problem (selecting a set of disjoint disks in the plane of maximum total weight) in disk graphs and for the maximum bisection problem (finding a partition of the vertex set into two subsets of equal cardinality with maximum number of edges between the subsets) in unit-disk graphs.
Research of the author was supported in part by the EU Thematic Network APPOL I + II, Approximation and Online Algorithms, IST-1999-14084 and IST-2001-32007.
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Keywords
- Planar Graph
- Intersection Graph
- Geometric Graph
- Polynomial Time Approximation Scheme
- Frequency Assignment
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References
Agarwal, P.K., van Kreveld, M., Suri, S.: Label placement by maximum independent set in rectangles. Computational Geometry 11, 209–218 (1998)
Arora, S., Karger, D., Karpinski, M.: Polynomial time approximation schemes for dense instances of NP-hard problems. Journal of Computer and System Science 58, 193–210 (1999)
Baker, B.: Approximation algorithms for NP-complete problems on planar graphs. Journal of the ACM 41, 153–180 (1994)
Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit disk graphs. Discrete Mathematics 86, 165–177 (1990)
Diaz, J., Kaminski, M.: Max-CUT and MAX-BISECTION are NP-hard on unit disk graphs. Theoretical Computer Science 377, 271–276 (2007)
Erlebach, T., Jansen, K., Seidel, E.: Polynomial-time approximation schemes for geometric graphs. SIAM Journal on Computing 34, 1302–1323 (2005)
Garey, M.R., Johnson, D.S., Stockmeyer, L.J.: Some simplified NP-complete graph problems. Theoretical Computer Science 1, 237–267 (1976)
Hadlock, F.: Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing 4, 221–225 (1975)
Hale, W.K.: Frequency assignment: theory and applications. Proceedings of the IEEE 68, 1497–1514 (1980)
Hlineny, P., Kratochvil, J.: Representing graphs by disks and balls. Discrete Mathematics 229, 101–124 (2001)
Hunt III, H.B., Marathe, M.V., Radhakrishnan, V., Ravi, S.S., Rosenkrantz, D.J., Stearns, R.E.: NC-approximation schemes for NP-and PSPACE-hard problems for geometric graphs. Journal of Algorithms 26, 238–274 (1998)
Jansen, K., Karpinski, M., Lingas, A., Seidel, E.: Polynomial time approximation schemes for max-bisection on planar and geometric graphs. SIAM Journal on Computing 35, 110–119 (2005)
Koebe, P.: Kontaktprobleme der konformen Abbildung, Berichteüber die Verhandlungen der Sächsischen Akademie der Wissenschaften. Leipzig, Math.-Phys. Klasse 88, 141–164 (1936)
Jerrum, M.: private communication (2000)
Malesinska, E.: Graph-theoretical models for frequency assignment problems, PhD thesis, Technische Universität Berlin (1997)
Marathe, M.V., Breu, H., Hunt III, H.B., Ravi, S.S., Rosenkrantz, D.J.: Simple heuristics for unit disk graphs. Networks 25, 59–68 (1995)
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Jansen, K. (2007). Approximation Algorithms for Geometric Intersection Graphs. In: Brandstädt, A., Kratsch, D., Müller, H. (eds) Graph-Theoretic Concepts in Computer Science. WG 2007. Lecture Notes in Computer Science, vol 4769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74839-7_15
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DOI: https://doi.org/10.1007/978-3-540-74839-7_15
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