Better approximation schemes for disk graphs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4059 LNCS, Issue , 2006, Pages 316-327

  Van Leeuwen, Erik Jan ^a  

^a CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; OPTIMIZATION; PROBLEM SOLVING; SET THEORY;

BOUNDED LEVEL DENSITY; DISK GRAPHS; GEOMETRIC GENERALIZATION; PLANAR GRAPHS;

GRAPH THEORY;

EID: 33746464501     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11785293_30     Document Type: Conference Paper

References (21)

1. Agarwal, P.K., Overmars, M., Sharir, M., "Computing maximally separated sets in the plane and independent sets in the intersection graph of unit disks" in SODA 2004, SIAM, 2004, pp. 516-525.
2. Alber, J., Fiala, J., "Geometric Separation and Exact Solutions for the Parameterized Independent Set Problem on Disk Graphs", J. Algorithms 52 2 (2003), pp. 134-151.
3. Baker, B.S., "Approximation Algorithms for NP-Complete Problems on Planar Graphs", JACM 41 1 (1994), pp. 153-180.
4. Chan, T.M., "Polynomial-time Approximation Schemes for Packing and Piercing Fat Objects", J. Algorithms 46 2 (2003), pp. 178-189.
5. Chan, T.M., "A Note on Maximum Independent Sets in Rectangle Intersection Graphs", Inf. Proc. Let. 89 1 (2004), pp. 19-23.
6. Clark, B.N., Colbourn, C.J., Johnson, D.S., "Unit Disk Graphs", Discr. Math. 86 1-3 (1990), pp. 165-177.
7. Eppstein, D., Miller, G.L., Teng, S.-H., "A Deterministic Linear Time Algorithm for Geometric Separators and its Applications", Funct. Inform. 22 4 (1995), pp. 309-329.
8. Erlebach, T., Jansen, K., Seidel, E., "Polynomial-time Approximation Schemes for Geometric Intersection Graphs" SIAM J. Computing 34 6 (2005), pp. 1302-1323.
9. Hochbaum, D.S., Maass, W., "Approximation Schemes for Covering and Packing Problems in Image Processing and VLSI", JACM 32 1 (1985), pp. 130-136.
10. Hunt III, D.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", J. Algorithms 26 2 (1998), pp. 238-274.
11. Koebe, P., "Kontaktprobleme der konformen Abbildung", Ber. Ver. Sächs. Ak. Wiss. Leipzig, Math.-Phys. Kl., 88 (1936), pp. 141-164.
12. Malesińska, E., Graph-Theoretical Models for Frequency Assignment Problems, PhD Thesis, Technical University of Berlin, Berlin, 1997.
13. Marathe, M.V., Breu, H., Hunt III, H.B., Ravi, S.S., Rosenkrantz, D.J., "Simple Heuristics for Unit Disk Graphs", Networks 25 (1995), pp. 59-68.
14. Marx, D., "Efficient Approximation Schemes for Geometric Problems?" in Proc. ESA 2005, LNCS 3669, Springer-Verlag, Berlin, 2005, pp. 448-459.
15. Matsui, T., "Approximation Algorithms for Maximum Independent Set Problems and Fractional Coloring Problems on Unit Disk Graphs", in Proc. JCDCG, LNCS 1763, Springer-Verlag, Berlin, 1998, pp. 194-200.
16. Miller, G.L., Teng, S.-H., Thurston, W., Vavasis, S.A., "Separators for Sphere-Packings and Nearest Neighbor Graphs", JACM 44 1 (1997), pp. 1-29.
17. Nieberg, T., Hurink, J.L., Kern, W., "A Robust PTAS for Maximum Weight Independent Sets in Unit Disk Graphs" in Proc. WG 2004, LNCS 3353, Springer-Verlag, Berlin, 2004, pp. 214-221.
18. Robertson, N., Seymour, P.D., "Graph Minors. I. Excluding a Forest", J. Comb. Th. B 35 (1983), pp. 39-61.
19. Telle, J.A., Proskurowski, A., "Algorithms for Vertex Partitioning Problems on Partial k-Trees", SIAM J. Disc. Math. 10 4 (1997), pp. 529-550.
20. van Leeuwen, E.J., Optimization Problems on Mobile Ad Hoc Networks - Algorithms for Disk Graphs, Master's Thesis INF/SCR-04-32, Inst. of Information and Computing Sciences, Utrecht Univ., 2004.
21. van Leeuwen, E.J., "Approximation Algorithms for Unit Disk Graphs" in Proc. WG 2005, LNCS 3787, Springer-Verlag, Berlin, 2005, pp. 351-361.