Fixed-parameter algorithms for the (k, r)-center in planar graphs and map graphs

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

Volumn 2719, Issue , 2003, Pages 829-844

  Demaine, Erik D ^a   Fomin, Fedor V ^b   Hajiaghayi, Mohammad Taghi ^a   Thilikos, Dimitrios M ^c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF BERGEN   (Norway)

^c UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DYNAMIC PROGRAMMING; GRAPHIC METHODS; MACHINERY; PARAMETER ESTIMATION;

CENTER PROBLEMS; DOMINATION PROBLEM; DYNAMIC PROGRAMMING ALGORITHM; FIXED-PARAMETER ALGORITHMS; FPT ALGORITHMS; GRAPH-THEORETIC; NUMBER OF CENTERS; TREE DECOMPOSITION;

GRAPH THEORY;

EID: 35248842524     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45061-0_65     Document Type: Article

References (27)

1. P. K. AGARWAL AND C. M. PROCOPIUC, Exact and approximation algorithms for clustering, Algorithmica, 33 (2002), pp. 201-226.
2. J. ALBER, H. L. BODLAENDER, H. FERNAU, T. KLOKS, AND R. NIEDERMEIER, Fixed parameter algorithms for dominating set and related problems on planar graphs, Algorithmica, 33 (2002), pp. 461-493.
3. J. ALBER, H. FERNAU, AND R. NIEDERMEIER, Parameterized complexity: Exponential speed-up for planar graph problems, in Electronic Colloquium on Computational Complexity (ECCC), Germany, 2001.
4. J. ALBER AND J. FIALA, Geometric separation and exact solutions for the parameterized independent set problem on disk graphs, in Foundations of Information Technology in the Era of Networking and Mobile Computing, IFIP 17th WCC/TCS'02, Montréal, Canada, vol. 223 of IFIP Conference Proceedings, Kluwer, 2002, pp. 26-37.
5. S. ARNBORG, J. LAGERGREN, AND D. SEESE, Problems easy for tree-decomposable graphs (extended abstract), in Automata, languages and programming (Tampere, 1988), Springer, Berlin, 1988, pp. 38-51.
6. B. S. BAKER, Approximation algorithms for NP-complete problems on planar graphs, J. Assoc. Comput. Mach., 41 (1994), pp. 153-180.
7. J. BAR-ILAN, G. KORTSARZ, AND D. PELEG, How to allocate network centers, J. Algorithms, 15 (1993), pp. 385-415.
8. Z.-Z. CHEN, Approximation algorithms for independent sets in map graphs, J. Algorithms, 41 (2001), pp. 20-40.
9. Z.-Z. CHEN, E. GRIGNI, AND C. H. PAPADIMITRIOU, Map graphs, J. ACM, 49 (2002), pp. 127-138.
10. B. COURCELLE, Graph rewriting: an algebraic and logic approach, in Handbook of theoretical computer science, Vol. B, Elsevier, Amsterdam, 1990, pp. 193-242.
11. 5-minor-free graphs, in The 13th Anual International Symposium on Algorithms and Computation-ISAAC 2002 (Vancouver, Canada), Springer, Lecture Notes in Computer Science, Berlin, vol.2518, 2002, pp. 262-273.
12. R. G. DOWNEY AND M. R. FELLOWS, Parameterized complexity, Springer-Verlag, New York, 1999.
13. D. EPPSTEIN, Diameter and treewidth in minor-closed graph families, Algorithmica, 27 (2000), pp. 275-291.
14. F. V. FOMIN AND D. M. THILIKOS, Dominating sets in planar graphs: Branch-width and exponential speed-up, in Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, 2003, pp. 168-177.
15. M. FRICK AND M. GROHE, Deciding first-order properties of locally tree-decomposable structures, J. Assoc. Comput. Mach., 48 (2001), pp. 1184-1206.
16. C. GAVOILLE, D. PELEG, A. RASPAUD, AND E. SOPENA, Small k-dominating sets in planar graphs with applications, in Graph-theoretic concepts in computer science (Boltenhagen, 2001), vol. 2204 of Lecture Notes in Comput. Sci., Springer, Berlin, 2001, pp. 201-216.
17. T. F. GONZALEZ, Clustering to minimize the maximum intercluster distance, Theoret. Comput. Sci., 38 (1985), pp. 293-306.
18. A. GUPTA AND N. NISHIMURA, Sequential and parallel algorithms for embedding problems on classes of partial k-trees, in Algorithm theory-SWAT '94 (Aarhus, 1994), vol. 824 of Lecture Notes in Comput. Sci., Springer, Berlin, 1994, pp. 172-182.
19. I. V. HICKS, Branch Decompositions and their applications, PhD thesis, Rice University, 2000.
20. I. KANJ AND L. PERKOVIĆ, Improved parameterized algorithms for planar dominating set, in Mathematical Foundations of Computer Science-MFCS 2002, Springer, Lecture Notes in Computer Science, Berlin, vol.2420, 2002, pp. 399-410.
21. T. KLOKS, C. M. LEE, AND J. LIU, New algorithms for k-face cover, k-feedback vertex set, and k-disjoint set on plane and planar graphs, in The 28th International Workshop on Graph-Theoretic Concepts in Computer Science(WG 2002), Springer, Lecture Notes in Computer Science, Berlin, vol. 2573, 2002, pp. 282-296.
22. J. PLESNÍK, On the computational complexity of centers locating in a graph, Apl. Mat., 25 (1980), pp. 445-452. With a loose Russian summary.
23. N. ROBERTSON AND P. D. SEYMOUR, Graph minors. X. Obstructions to tree-decomposition, J. Combin. Theory Ser. B, 52 (1991), pp. 153-190.
24. N. ROBERTSON, P. D. SEYMOUR, AND R. THOMAS, Quickly excluding a planar graph, J. Combin. Theory Ser. B, 62 (1994), pp. 323-348.
25. P. D. SEYMOUR AND R. THOMAS, Call routing and the ratcatcher, Combinatorica, 14 (1994), pp. 217-241.
26. C. SWAMY AND A. KUMAR, Primal-dual algorithms for connected facility location problems, in Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization, vol. 2462 of Lecture Notes in Computer Science, Rome, Italy, September 2002, pp. 256-270.
27. M. THORUP, Map graphs in polynomial time, in The 39th Annual Symposium on Foundations of Computer Science (FOCS 1998), IEEE Computer Society, 1998, pp. 396-405.