Planarity allowing few error vertices in linear time

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2009, Pages 639-648

  Kawarabayashi, Ken Ichi ^a  

^a NATIONAL INSTITUTE OF INFORMATICS   (Japan)

Author keywords

Approximation algorithms and linear time; Few errors; Planarity; TSP

Indexed keywords

APEX GRAPH; CROSSING NUMBER; FEW ERRORS; FIXED SURFACES; INPUT GRAPHS; LINEAR TIME; LINEAR-TIME ALGORITHMS; LINEAR-TIME APPROXIMATION; MINIMUM VALUE; NOT GIVEN; NP COMPLETE; PLANAR GRAPH; PLANARITY; TSP; VERTEX SET;

COMPUTER SCIENCE; ERRORS; FIBER OPTIC CHEMICAL SENSORS; GRAPH THEORY; GRAPHIC METHODS; MATHEMATICAL TECHNIQUES; SURFACE TESTING;

APPROXIMATION ALGORITHMS;

EID: 77952327518     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2009.45     Document Type: Conference Paper

References (48)

1. S. Arnborg and A. Proskurowski, Linear time algorithms for NP-hard problems restricted to partial k-trees, Discrete Appl. Math. 23 (1989), 11-24.
2. S. Arora, M. Grigni, D. Karger, P. Klein and A. Woloszyn, A polynomial-time approximation scheme for weighted planar graph TSP, Proc. 9th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'98), 33-41, (1998).
3. I. Adler, M. Grohe and S. Kreutzer, Computing excluded minors, Proc. 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'08), 641-650, (2008).
4. B. S. Baker, Approximation algorithms for NP-complete problems on planar graphs, J. ACM, 41 (1994), 153-180.
5. A. Berger, A. Czumaj, M. Grigni and H. Zhao, Approximation schemes for minimum 2-connected spanning subgraphs in weighted planar graphs, Proc. 13th Annual European Symposium on Algorithms, 3669, Lecture Notes in Computer Science, 472-483, (2005).
6. J. A. Bondy and U. S. R. Murty, Graph Theory, Springer, 2008.
7. K. S. Booth and G.S. Lueker, Testing for the consecutive ones property, interval graphs and graph planarity using PQ-trees, J. Comput. System Sci., 13 (1976), 335-379.
8. H. L. Bodlaender, A linear-time algorithm for finding tree-decomposition of small treewidth, SIAM J. Comput., 25 (1996), 1305-1317.
9. S. Cabello and B. Mohar, Problem of months, Fall 2005, http://www.fmf.uni-lj.si/~mohar/
10. N. Chiba, T. Nishizeki, S. Abe and T. Ozawa, A linear time algorithm for embedding planar graphs using PQ-trees, J. Comput. System Sci., 30 (1985), 54-76.
11. A. Czumaj, M. Grigni, P. Sissokho and H. Zhao, Approximation schemes for minimum 2-edge-connected and bicon-nected subgraphs in planar graphs. Proc. 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'04), 496-505, (2004).
12. E. D. Demaine, F. Fomin, M. Hajiaghayi, and D. Thilikos, Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs, J. ACM, 52 (2005), 1-29.
13. E. D. Demaine, M. Hajiaghayi, and K. Kawarabayashi, Algorithmic graph minor theory: Decomposition, approximation and coloring, Proc. 46th Symposium on Foundations of Computer Science, (FOCS'05), 637-646, (2005).
14. E. D. Demaine, M. Hajiaghayi, and B. Mohar, Approximation algorithms via contraction decomposition, Proc. 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'07), 278-287, (2007).
15. R. Diestel, K. Yu. Gorbunov, T. R. Jensen, and C. Thomassen, Highly connected sets and the excluded grid theorem, J. Combin. Theory Ser. B, 75 (1999), 61-73.
16. R. Diestel, K. Kawarabayashi and P. Wollan, The Erdos-Pósa property for clique minors in highly connected graphs, submitted.
17. R.G. Downey and M.R. Fellows, Parameterized complexity, Springer-Verlag, 1999.
18. D. Eppstein, Subgraph isomorphism in planar graphs and related problems, J. Graph Algor. Appl., 3 (1999), 1-27.
19. D. Eppstein, Diameter and tree-width in minor-closed graph families, Algorithmica, 27 275-291, (2000).
20. M.R. Fellows and M. A. Langston, On serach, decision and the efficiency of polynomial time algorithms (extended abstract), Proc. 21th ACM Symposium on Theory of Computing (STOC'89), 501-512, (1989).
21. M. Grigni, E. Koutsoupias, and C. Papadimitriou, An approximation scheme for planar graphs TSP, Proc. 36th Symposium on Foundations of Computer Science, (FOCS'95), 640-646, (1995).
22. M. Grohe, Local tree-width, excluded minors, and approximation algorithms. Combinatorica 23, (2003), 613-632.
23. J. E. Hopcroft and R. E. Tarjan, Dividing a graph into triconnected components, Siam J. Comput., 3 (1973), 135-158.
24. J. E. Hopcroft and R. Tarjan, Efficient planarity testing, J. ACM, 21 (1974), 549-568.
25. K. Kawarabayashi and B. Reed, Computing crossing number in linear time, Proc. 39th ACM Symposium on Theory of Computing (STOC'07), 382-390, (2007).
26. K. Kawarabayashi and B. Mohar, Graph and Map Isomorphism and all polyhedral embeddings in linear time, Proc. 40th ACM Symposium on Theory of Computing (STOC'08), 471-480, (2008).
27. K. Kawarabayashi, B. Mohar and B. Reed, A simpler linear time algorithm for embedding graphs into an arbitrary surface and the genus of bounded tree-width graphs, Proc. 49th Annual Symposium on Foundations of Computer Science (FOCS'08), 771-780, (2008).
28. 6 minors in large 6-connected graphs, submitted.
29. P. N. Klein, A linear time approximation scheme for TSP for planar wieghted graphs, Proc. 46th Symposium on Foundations of Computer Science (FOCS'05), 146-155, (2005).
30. J. M. Lewis and M. Yannakakis, The vertex-deletion problem for hereditary propeties is NP-complete, J. Comput. System Sci., 20 (1980), 219-230.
31. R.J. Lipton and R. E. Tarjan, Applications of a planar separator theorem, Siam J. Comput., 9 (1980), 615-627.
32. D. Marx and I. Schlotter, Obtaining a planar graph by vertex deletion, Proc. the 33rd Workshop on Graph-Theoretic Concepts in Computer Scienece, (2007), 292-303.
33. B. Mohar, Embedding graphs in an arbitrary surface in linear time, Proc. 28th ACM Symposium on Theory of Computing (STOC'96), 392-397, (1996).
34. B. Mohar, A linear time algorithm for embedding graphs in an arbitrary surface, SIAM J. Discrete Math., 12 (1999), 6-26.
35. B. Mohar, Face covers and the genus of apex graphs, J. Combin. Theory Ser. B, 82 (2001), 102-117.
36. B. Mohar, A. Schrijver, Blocking nonorientability of a surface, J. Combin. Theory Ser. B 87 (2003), 2-16.
37. B. Mohar and C. Thomassen, Graphs on Surfaces, Johns Hopkins University Press, Baltimore, MD, 2001.
38. L. Perković and B. Reed, An improved algorithm for finding tree decompositions of small width, International Journal on the Foundations of Computing Science, 11 (2000), 81-85.
39. B. Reed, Tree width and tangles: a new connectivity measure and some applications, in "Surveys in Combinatorics, 1997 (London)", London Math. Soc. Lecture Note Ser. 241, Cambridge Univ. Press, Cambridge, 87-162, (1997).
40. B. Reed, Rooted Routing in the Plane, Discrete Appl. Math., 57 (1995), 213-227.
41. B. Reed, N. Robertson, A. Schrijver and P. D. Seymour, Finding disjoint trees in planar graphs in linear time. Graph structure theory (Seattle, WA, 1991), 295-301, Contemp. Math. 147, Amer. Math. Soc., Providence, RI, 1993.
42. B. Reed and D. Wood, A linear time algorithm to find a separator in a graph with an excluded minor, submitted.
43. N. Robertson and P. D. Seymour, Graph minors. V. Excluding a planar graph, J. Combin. Theory Ser. B, 41 (1986), 92-114.
44. N. Robertson and P. D. Seymour, Graph minors. XIII. The disjoint paths problem, J. Combin. Theory Ser. B, 63 (1995), 65-110.
45. N. Robertson and P. D. Seymour, Graph minors. XVI. Excluding a non-planar graph, J. Combin. Theory Ser. B, 89 (2003), 43-76.
46. N. Robertson, P. D. Seymour and R. Thomas, Quickly excluding a planar graph, J. Combin. Theory Ser. B, 62 (1994), 323-348.
47. C. Thomassen, The graph genus problem is NP-complete, J. Algorithms 10 458-476, (1988).
48. S. G. Williamson, Depth-first search and Kuratowski subgraphs, J. ACM 31 (1984), 681-693.