On graph isomorphism for restricted graph classes

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

Volumn 3988 LNCS, Issue , 2006, Pages 241-256

  Köbler, Johannes ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ALGORITHMS; COMPUTATIONAL COMPLEXITY; FORMAL LOGIC; PROBLEM SOLVING;

ALGORITHMIC PROBLEMS; COMBINATORICS; GRAPH CLASSES; GRAPH ISOMORPHISM (GI);

GRAPH THEORY;

EID: 33746086721     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11780342_26     Document Type: Conference Paper

References (49)

1. M. Agrawal and N. Saxena. Automorphisms of finite rings and applications to complexity of problems. In Proc. 22nd Symposium on Theoretical Aspects of Computer Science, volume 3404 of Lecture Notes in Computer Science, pages 1-17. Springer-Verlag, Berlin Heidelberg, 2005.
2. C. Àlvarez and B. Jenner. A very hard log-space counting class. Theoretical Computer Science, 107(1):3-30, 1993.
3. V. Arvind and J. Köhler. Hypergraph isomorphism testing for bounded color classes. In Proc. 23rd Symposium on Theoretical Aspects of Computer Science, volume 3884 of Lecture Notes in Computer Science, pages 384-395. Springer-Verlag, Berlin Heidelberg, 2006.
4. V. Arvind, P. Kurur, and T. Vijayaraghavan. Bounded color multiplicity graph isomorphism is in the #L hierarchy. In Proc. 20th Annual IEEE Conference on Computational Complexity, pages 13-27. IEEE Computer Society Press, 2005.
5. V. Arvind and J. Torán. Isomorphism testing: Pespective and open problems. Bulletin of the European Association of Theoretical Computer Science (BEATCS), 86, 2005.
6. L. Babai. Moderately exponential bounds for graph isomorphism. In Proc. International Symposium on Fundamentals of Computing Theory 81, volume 117 of Lecture Notes in Computer Science, pages 34-50. Springer-Verlag, Berlin Heidelberg, 1981.
7. L. Babai. Trading group theory for randomness. In Proc. 17th ACM Symposium on Theory of Computing, pages 421-429. ACM Press, 1985.
8. L. Babai. A Las Vegas-NC algorithm for isomorphism of graphs with bounded multiplicity of eigenvalues. In Proc. 27th IEEE Symposium on the Foundations of Computer Science, pages 303-312. IEEE Computer Society Press, 1986.
9. L. Babai. Automorphism groups, isomorphism, reconstruction. In R. L. Graham, M. Grötschel, and L. Lovász, editors, Handbook of Combinatorics, pages 1447-1540. Elsevier Science Publishers, 1995.
10. L. Babai, D. Grigoryev, and D. Mount. Isomorphism of graphs with bounded eigenvalue multiplicity. In Proc. 14th ACM Symposium on Theory of Computing, pages 310-324. ACM Press, 1982.
11. L. Babai and E. Luks. Canonical labeling of graphs. In Proc. 15th ACM Symposium on Theory of Computing, pages 171-183, 1983.
12. L. Babai, E. Luks, and A. Seress. Permutation groups in NC. In Proc. 19th ACM Symposium on Theory of Computing, pages 409-20. ACM Press, 1987.
13. J. L. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity I. EATCS Monographs on Theoretical Computer Science. Springer-Verlag, Berlin Heidelberg, second edition, 1995.
14. H. Bodlaender. Polynomial algorithm for graph isomorphism and chromatic index on partial k-trees. Journal of Algorithms, 11:631-643, 1990.
15. K. Booth. Isomorphism testing for graphs, semigroups, and finite automata are polynomially equivalent problems. SIAM Journal on Computing, 7(3):273-279, 1978.
16. R. Boppana, J. Hastad, and S. Zachos. Does co-NP have short interactive proofs? Information Processing Letters, 25(2):27-32, 1987.
17. G. Buntrock, C. Damm, U. Hertrampf, and C. Meinel. Structure and importance of logspace-MOD classes. Mathematical Systems Theory, 25:223-237, 1992.
18. S. Buss. Alogtime algorithms for tree isomorphism, comparison, and canonization. In Computational Logic and Proof Theory, 5th Kurt Gödel Colloquium'97, volume 1289 of Lecture Notes in Computer Science, pages 18-33. Springer-Verlag, Berlin Heidelberg, 1997.
19. J. Cai, M. Fürer, and N. Immerman. An optimal lower bound for the number of variables for graph identification. Combinatorica, 12:389-410, 1992.
20. S. A. Cook. A taxonomy of problems with fast parallel algorithms. Information and Control, 64:2-22, 1985.
21. S. Evdokimov, M. Karpinski, and I. Ponomarenko. On a new high dimensional Weisfeiler-Lehman algorithm. Journal of Algebraic Combinatorics, 10:29-45, 1999.
22. M. Furst, J. Hopcroft, and E. Luks. Polynomial time algorithms for permutation groups. In Proc. 21st IEEE Symposium on the Foundations of Computer Science, pages 36-41. IEEE Computer Society Press, 1980.
23. M. Grohe. Fixed-points logics on planar graphs. In Proceedings of the 13th Symposium on Logic in Computer Science, pages 6-15, 1998.
24. M. Grohe. Isomorphism testing for ernbeddable graphs through definability. In Proc. 32th ACM Symposium on Theory of Computing, pages 63-172, 2000.
25. M. Grohe and J. Mariño. Definability and descriptive complexity on databases of bounded tree-width. In C. Beeri and P. Bunemann, editors, Proceedings of the, 7th Conference on Database Theory, volume 1540, pages 70-82. Springer-Verlag, Berlin Heidelberg, 1999.
26. M. Grohe and O. Verbitsky. Testing graph isomorphism in parallel by playing a game. Manuscript, 2006.
27. Y. Gurevich. From invariants to canonization. Bulletin of the European Association of Theoretical Computer Science (BEATCS), 63, 1997.
28. J. E. Hopcroft and R. E. Tarjan. Isomorphism of planar graphs (working paper). In R. Miller and J. Thatcher, editors, Complexity of computer computations, pages 131-152. Plenum Press, New York-London, 1972.
29. J. E. Hopcroft and R. E. Tarjan. Efficient planarity testing. Journal of the ACM, 21:549-568620, 1974.
30. J. E. Hopcroft and J. Wong. Linear time algorithm for isomorphisms of planar graphs. Proc. 6th ACM Symposium on Theory of Computing, pages 172-184, 1974.
31. N. Immerman. Number of quantifiers is better than number of tape cells. Journal of Computer and System Sciences, 22(3):384-406, 1981.
32. R. Impagliazzo and L. A. Levin. No better ways to generate hard NP-instances than picking uniformly at random. In Proc. 31st IEEE Symposium on the Foundations of Computer Science, pages 812-821. IEEE Computer Society Press, 1990.
33. J. M. I.S. Filotti. A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus. In Proc. 12th ACM Symposium on Theory of Computing, pages 236-243. ACM Press, 1980.
34. B. Jenner, J. Köhler, P. McKenzie, and J. Torán. Completeness results for graph isomorphism. Journal of Computer and System Sciences, 66:549-566, 2003.
35. J. Köhler, U. Schöning, and J. Toràn. The Graph Isomorphism Problem: Its Structural Complexity. Progress in Theoretical Computer Science. Birkhäuser, Boston, 1993.
36. D. Lichtenstein. Isomorphism for graphs embaddable on the projective plane. In Proc. 12th ACM Symposium on Theory of Computing, pages 218-224. ACM Press, 1980.
37. S. Lindell. A logspace algorithm for tree canonization. In Proc. 24th ACM Symposium on Theory of Computing, pages 400-404. ACM Press, 1992.
38. E. Luks. Isomorphism of bounded valence can be tested in polynomial time. Journal of Computer and System Sciences, 25:42-65, 1982.
39. E. Luks. Parallel algorithms for permutation groups and graph isomorphism. In Proc. 27th IEEE Symposium on the Foundations of Computer Science, pages 292-302. IEEE Computer Society Press, 1986.
40. R. Mathon. A note on the graph isomorphism counting problem. Information Processing Letters, 8:131-132, 1979.
41. G. Miller. Isomorphism testing for graphs of bounded genus. In Proc. 12th ACM Symposium on Theory of Computing, pages 225-235. ACM Press, 1980.
42. G. Miller and J. Reif. Parallel tree contraction, part 2: Further applications. SIAM Journal on Computing, 20:1128-1147, 1991.
43. I. Ponomarenko. The isomorphism problem for classes of graphs that are invariant with respect to contraction (Russian). Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 174:147-177, 1988.
44. O. Reingold. Undirected st-connectivity in log-space. In Proc. 37th ACM Symposium on Theory of Computing, pages 376-385. ACM Press, 2005.
45. U. Schöning. Graph isomorphism is in the low hierarchy. Journal of Computer and System Sciences, 37:312-323, 1988.
46. S. Toda. PP is as hard as the polynomial-time hierarchy. SIAM Journal on Computing, 20:865-877, 1991.
47. J. Torán. On the hardness of graph isomorphism. SIAM Journal on Computing, 33(5): 1093-1108, 2004.
48. V. N. Zemlyachenko. Canonical numbering of trees (Russian). Proc. Seminar on Comb. Anal. at Moscow State University, 1970.
49. V. N. Zemlyachenko, N. Konienko, and R. I. Tyshkevich. Graph isomorphism problem (Russian). The Theory of Computation I, Notes Sci. Sem. LOMI 118, 1982.