Logo

Login

Isomorphic Subgraphs

Bachl, Sabine (1999) Isomorphic Subgraphs. [Conference Paper]

Full text not available from this repository.

Abstract

We are interested in finding symmetries in graphs and then use these symmetries for graph drawing algorithms. There are two general approaches to this problem, the first one is known as GEOMETRIC SYMMETRIES on the basis of drawings, the other rests upon the graph-theoretical notion of graphs. For a given graph G the ISOMORPHIC SUBGRAPHS problem makes use of the second approach and tries to find the two largest disjoint isomorphic subgraphs in G. Hence, G consists of two identical copies and a remainder. There are many NP-complete or open problems related to our problem, like GRAPH ISOMORPHISM, GRAPH AUTOMORPHISM or LARGEST COMMON SUBGRAPH. We show that the ISOMORPHIC SUBGRAPHS problem is NP-hard for connected outerplanar graphs, and 2-connected planar graphs and is solvable in linear time when restricted to trees. Additionally we will shortly discuss the applicability of ISOMORPHIC SUBGRAPHS in graph drawing algorithms.

Item Type:Conference Paper
Classifications:G Algorithms and Complexity > G.910 Symmetries
G Algorithms and Complexity > G.999 Others
ID Code:357
Deposited By:Maciejak, Agnes
Deposited On:23 Nov 2004
Last Modified:18 Sep 2008 13:08
Alternative Locations:http://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=1731&spage=286

Repository Staff Only: item control page

References

[1] W. Bachl. Entwicklung und Implementierung eines Hierarchischen Springembedders. Diplomarbeit, Universität Passau, 1995.

[2] F. J. Brandenburg. Designing graph drawings by layout graph grammars. In Proc. Graph Drawing 1994, Lecture Notes in Computer Science 894, pages 416-427. Springer, 1995.

[3] F. J. Brandenburg and S. Wetzel. On pairs of large common subgraphs. Unpublished manuscript, http://www.fmi.uni-passau.de/~wetzel/paper/, 1998.

[4] Qing-Wen Feng, Robert F. Cohen, and Peter Eades. How to draw a planar clustered graphs. In Ding-Zhu Du and Ming Li, editors, Computing and Combinatorics COCOON '95, Lecture Notes in Computer Science 959, pages 21-30. Springer, 1995.

[5] Qing-Wen Feng, Robert F. Cohen, and Peter Eades. Planarity for clustered graphs. In Paul Spirakis, editor, Algorithms-ESA '95, Lecture Notes in Computer Science 979, pages 213-226. Springer, 1995.

[6] M. R. Garey and D. S. Johnson. Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979.

[7] D. Gusfield. Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, 1997.

[8] R. E. Ladner. On the structure of polynomial time reducibility. Journal of the ACM, 22:155-171, 1975.

[9] Giorgio Levi and Fabrizio Luccio. A technique for graph embedding with constraints on node and arc correspondences. Information Sciences, 5:1-24, 1973.

[10] Andrzej Lingas. Subgraph isomorphism for biconnected outerplanar graphs in cubic time. Theoretical Computer Science, 63:295-302, 1989.

[11] R. J. Lipton, S. C. North, and J. S. Sandberg. A method for drawing graphs. In Proc. ACM Symposium on Computational Geometry, pages 153-160. ACM, 1985.

[12] A. Lubiw. Some NP-complete problems similar to graph isomorphism. SIAM J. Comput., 10(1):11-21, 1981.

[13] J. Manning. Geometric Symmetry in graphs. PhD thesis, Department of Computer Science, Purdue University, 1990.

[14] J. Manning and M. J. Atallah. Fast detection and display of symmetry in trees. Congressus Numerantium 64:159-168, 1988.

[15] J. Manning and M. J. Atallah. Fast detection and display of symmetry in outerplanar graphs. Discrete Applied Mathematics, 39:13-35, 1992.

[16] H. Purchase. Which aesthetic has the greatest effect on human understanding. In Proc. Graph Drawing 1997, Lecture Notes in Computer Science 1353, pages 248-261. Springer, 1997.

[17] H. C. Purchase, R. F. Cohen, and M. James. Validating graph drawing aesthetics. In Proc. Graph Drawing 1995, Lecture Notes in Computer Science 1027, pages 435-446. Springer, 1996.

[18] Ronald C. Read and Derek G. Corneil. The graph isomorphism disease. Journal of Graph Theory, 1:339-363, 1977.

[19] Steven W. Reyner. An analysis of a good algorithm for the subtree problem. SIAM J. Comput., 6(4):730-732, 1977.

[20] U. Schöning. Graph isomorphism is in the low hierarchy. Journal. Comput. Syst. Science, 37:312-323, 1987.

[21] Maciej M. Syslo. The subgraph isomorphism problem for outerplanar graphs. Theoretical Computer Science, 17:91-97, 1982.

[22] E. Ukkonen. On-line construction of suffix-trees. In Algorithmica 14, pages 249-260, 1995.

[23] P. Weiner. Linear pattern matching algorithms. In Proc. of the 14th IEEE Symp. on Switching and Automata Theory, pages 1-11, 1973.

[24] F. Frances Yao. Graph 2-isomorphism is NP-complete. Information Processing Letters, 9(2):68-72, August 1979.

GDEA is powered by EPrints 3 which is developed by the School of Electronics and Computer Science at the University of Southampton. More information and software credits.