Approximation algorithms via contraction decomposition

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 07-09-January-2007, Issue , 2007, Pages 278-287

  Demaine, Erik D ^a   Hajiaghayi, MohammadTaghi ^b   Mohar, Bojan ^c,d  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b Carnegie Mellon University   (United States)

^c SIMON FRASER UNIVERSITY   (Canada)

^d UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; GRAPHIC METHODS; TRAVELING SALESMAN PROBLEM;

BOUNDED TREEWIDTH; BOUNDED-GENUS GRAPHS; FREE GRAPHS; GENERAL CLASS; OPTIMAL SOLUTIONS; PLANAR GRAPH;

APPROXIMATION ALGORITHMS;

EID: 84969219565     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (42)

1. [AGK+98] Sanjeev Arora, Michelangelo Grigni, David Karger, Philip Klein, and Andrzej Woloszyn. A polynomial-time approximation scheme for weighted planar graph TSP. In Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 33-41, 1998.
2. [Ami01] Eyal Amir. Efficient approximation for triangulation of minimum treewidth. In Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence (UAI-2001), pages 7-15, San Francisco, CA, 2001. Morgan Kaufmann Publishers.
3. [ARV04] Sanjeev Arora, Satish Rao, and Umesh Vazirani. Expander flows, geometric embeddings and graph partitioning. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pages 222-231, 2004.
4. [Bak94] Brenda S. Baker. Approximation algorithms for NP-complete problems on planar graphs. Journal of the Association for Computing Machinery, 41(1):153-180, 1994.
5. [BCGZ05] André Berger, Artur Czumaj, Michelangelo Grigni, and Hairong Zhao. Approximation schemes for minimum 2-connected spanning subgraphs in weighted planar graphs. In Proceedings of the 13th Annual European Symposium on Algorithms 3669 of Lecture Notes in Computer Science, pages 472-483, Palma de Mallorca, Spain, October 2005.
6. [BMR96] Richard Brunet, Bojan Mohar, and R. Bruce Richter. Separating and nonseparating disjoint homotopic cycles in graph embeddings. Journal of Combinatorial Theory. Series B, 66(2):201-231, 1996.
7. [Bod05] Hans L. Bodlaender. Discovering treewidth. In Proceedings of the 31st Conference on Current Trends in Theory and Practice of Computer Science, volume 3381 of Lecture Notes in Computer Science, pages 1-16, Liptovský Ján, Slovakia, January 2005.
8. [CGSZ04] Artur Czumaj, Michelangelo Grigni, Papa Sissokho, and Hairong Zhao. Approximation schemes for minimum 2-edge-connected and biconnected subgraphs in planar graphs. In Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 496-505, Philadelphia, PA, USA, 2004. Society for Industrial and Applied Mathematics.
9. [CM05] Sergio Cabello and Bojan Mohar. Finding shortest non-separating and non-contractible cycles for topologically embedded graphs. In Proceedings of the 13th Annual European Symposium on Algorithms volume 3669 of Lecture Notes in Computer Science, pages 131-142, Palma de Mallorca, Spain, October 2005.
10. [DDO+04] Matt De Vos, Guoli Ding, Bogdan Oporowski, Daniel P. Sanders, Bruce Reed, Paul Seymour, and Dirk Vertigan. Excluding any graph as a minor allows a low tree-width 2-coloring. Journal of Combinatorial Theory, Series B, 91(1):25-41, 2004.
11. [DFHT04] Erik D. Demaine, Fedor V. Fomin, Mohammad-Taghi Hajiaghayi, and Dimitrios M. Thilikos. Bidimensional parameters and local treewidth. SIAM Journal on Discrete Mathematics, 18(3):501-511, December 2004.
12. [DFHT05a] Erik D. Demaine, Fedor V. Fomin, Mohammad-Taghi Hajiaghayi, and Dimitrios M. Thilikos. Fixedparameter algorithms for (k, r)-center in planar graphs and map graphs. ACM Transactions on Algorithms, 1(1):33-47, 2005.
13. [DFHT05b] Erik D. Demaine, Fedor V. Fomin, Mohammad Taghi Hajiaghayi, and Dimitrios M. Thilikos. Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs. Journal of the ACM, 52(6):866-893, 2005.
14. [DFT06] Frederic Dorn, Fedor V. Fomin, and Dimitrios M. Thilikos. Fast subexponential algorithm for non-local problems on graphs of bounded genus. In Proceedings of the 10th Scandinavian Workshop on Algorithm Theory, Riga, Latvia, July 2006. To appear.
15. [DH04a] Erik D. Demaine and Mohammad Taghi Hajiaghayi. Diameter and treewidth in minor-closed graph families, revisited. Algorithmica, 40(3):211-215, August 2004.
16. [DH04b] Erik D. Demaine and Mohammad Taghi Hajiaghayi. Equivalence of local treewidth and linear local treewidth and its algorithmic applications. In Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA'04), pages 833-842, January 2004.
17. [DHK05] Erik D. Demaine, Mohammad Taghi Hajiaghayi, and Kenichi Kawarabayashi. Algorithmic graph minor theory: Decomposition, approximation, and coloring. In Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, pages 637-646, Pittsburgh, PA, October 2005.
18. [DHN+04] Erik D. Demaine, Mohammad Taghi Hajiaghayi, Naomi Nishimura, Prabhakar Ragde, and Dimitrios M. Thilikos. Approximation algorithms for classes of graphs excluding single-crossing graphs as minors. Journal of Computer and System Sciences, 69(2):166-195, September 2004.
19. [DHT06] Erik D. Demaine, Mohammad Taghi Hajiaghayi, and Dimitrios M. Thilikos. The bidimensional theory of bounded-genus graphs. SIAM Journal on Discrete Mathematics, 20(2):357-371, 2006.
20. [Epp00] David Eppstein. Diameter and treewidth in minorclosed graph families. Algorithmica, 27(3-4):275-291, 2000.
21. [FK98] Uriel Feige and Joe Kilian. Zero knowledge and the chromatic number. Journal of Computer and System Sciences, 57(2):187-199, 1998.
22. [FT04] Fedor V. Fomin and Dimitrios M. Thilikos. Fast parameterized algorithms for graphs on surfaces: Linear kernel and exponential speed-up. In Proceedings of the 31st International Colloquium on Automata, Languages and Programming (ICALP 2004), pages 581-592, Turku, Finland, July 2004.
23. [GHT84] John R. Gilbert, Joan P. Hutchinson, and Robert Endre Tarjan. A separator theorem for graphs of bounded genus. J. Algorithms, 5(3):391-407, 1984.
24. [GKP95] Michelangelo Grigni, Elias Koutsoupias, and Christos Papadimitriou. An approximation scheme for planar graph TSP. In Proceedings of the 36th Annual Symposium on Foundations of Computer Science (Milwaukee, WI, 1995), pages 640-645, Los Alamitos, CA, 1995.
25. [Gri00] Michelangelo Grigni. Approximate TSP in graphs with forbidden minors. In Proceedings of the 27th International Colloquium of Automata, Languages and Programming (Geneva, 2000), volume 1853 of Lecture Notes in Computer Science, pages 869-877. Springer, Berlin, 2000.
26. [Gro03] Martin Grohe. Local tree-width, excluded minors, and approximation algorithms. Combinatorica, 23(4):613-632, 2003.
27. [GS02] Michelangelo Grigni and Papa Sissokho. Light spanners and approximate TSP in weighted graphs with forbidden minors. In Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 852-857, 2002.
28. [Kel06] Jonathan A. Kelner. Spectral partitioning, eigenvalue bounds, and circle packings for graphs of bounded genus. SIAM Journal on Computing, 35(4):882-902 (electronic), 2006.
29. [Kle05] Philip N. Klein. A linear-time approximation scheme for TSP for planar weighted graphs. In Proceedings of the 46th IEEE Symposium on Foundations of Computer Science, pages 146-155, 2005.
30. [Kle06] Philip N. Klein. A subset spanner for planar graphs, with application to subset TSP. In Proceedings of the 38th ACM Symposium on Theory of Computing, 2006. to appear.
31. [LR99] Tom Leighton and Satish Rao. Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms. Journal of the ACM, 46(6):787-832, 1999.
32. [LT80] Richard J. Lipton and Robert Endre Tarjan. Applications of a planar separator theorem. SIAM Journal on Computing, 9(3):615-627, 1980.
33. [Moh92] Bojan Mohar. Combinatorial local planarity and the width of graph embeddings. Canadian Journal of Mathematics, 44(6):1272-1288, 1992.
34. [Moh99] Bojan Mohar. A linear time algorithm for embedding graphs in an arbitrary surface. SIAM Journal on Discrete Mathematics, 12(1):6-26, 1999.
35. [Moh01] Bojan Mohar. Graph minors and graphs on surfaces. In Surveys in Combinatorics, volume 288 of London Math. Soc. Lecture Note Ser., pages 145-163. Cambridge Univ. Press, Cambridge, 2001.
36. [MT01] Bojan Mohar and Carsten Thomassen. Graphs on surfaces. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, MD, 2001.
37. [RS86] Neil Robertson and Paul D. Seymour. Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms, 7(3):309-322, 1986.
38. [RS94] Neil Robertson and P. D. Seymour. Graph minors. XI. Circuits on a surface. Journal of Combinatorial Theory, Series B, 60(1):72-106, 1994.
39. [RS03] Neil Robertson and P. D. Seymour. Graph minors. XVI. Excluding a non-planar graph. Journal of Combinatorial Theory, Series B, 89(1):43-76, 2003.
40. [Tho95] Robin Thomas. Problem Session of the 3rd Solvene Conference on Graph Theory, Bled, Slovenia, 1995.
41. [Tho98] Mikkel Thorup. All structured programs have small tree-width and good register allocation. Information and Computation, 142(2):159-181, 1998.
42. [Wag37] K. Wagner. Über eine Eigenschaft der eben Komplexe. Mathematische Annalen, 114:570-590, December 1937.