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On the coding of ordered graphs

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Abstract

Ordered graph and ordered graph isomorphism provide a natural representation of many objects in applications such as computational geometry, computer vision and pattern recognition. In the present paper we propose a coding procedure for ordered graphs that improves an earlier one based on Eulerian circuits of graphs in terms of both simplicity and computational efficiency. Using our coding approach, we show that the ordered graph isomorphism problem can be optimally solved in quadratic time, although no efficient (polynomial-bound) isomorphism algorithm for general graphs exists today. An experimental evaluation demonstrates the superior performance of the new method.

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References

  1. Gati G.: Further annotated bibliography on the isomorphism disease. J. Graph Theory3, 95–109 (1979).

    Article  MATH  Google Scholar 

  2. Hopcroft, J. E., Tarjan, R. E.: AVlogV algorithm for isomorphism of triconnected planar graphs. J. Comput. Syst. Sci.7, 323–331 (1973).

    MATH  Google Scholar 

  3. Hopcroft, J. E., Wong, J. K.: Linear time algorithm for isomorphism of planar graphs. Proc. of 6th Annual ACM Symposium on Theory of Computing, pp. 172–184, 1974.

  4. Jiang, X., Bunke, H.: Optimal quadratic-time isomorphism of ordered graphs. Technical Report, Department of Computer Science, University of Bern, 1997.

  5. Luks, E. M.: Isomorphism of graphs of bounded valence can be tested in polynomial time. J. Comput. Syst. Sci.25, 42–65 (1982).

    Article  MATH  Google Scholar 

  6. Read, R. C.: The coding of various kinds of unlabeled trees. In: Graph theory and computing (Read, R.C. ed.), pp. 153–182. New York: Academic Press 1972.

    Google Scholar 

  7. Read, R. C., Corneil, D. G.: The graph isomorphism disease. J. Graph Theory1, 339–363 (1977).

    Article  MATH  Google Scholar 

  8. Schöning, U.: Graph isomorphism is in the low hierarchy. J. Comput. Syst. Sci.37, 312–323 (1988).

    Article  MATH  Google Scholar 

  9. Ullmann, J. R.: An algorithm for subgraph isomorphism. J. Assoc. Comput. Mach.23, 31–42 (1976).

    Google Scholar 

  10. Weinberg, L.: Plane representations and codes for planar graphs. Proc. of Third Annal Allerton Conf. on Circuit and System Theory, pp. 733–744, 1965.

  11. Weinberg, L.: A simple and efficient algorithm for determining isomorphism of planar triply connected graphs. IEEE Trans. Circuit Theory13, 142–148 (1966).

    Google Scholar 

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  1. Department of Computer Science, University of Bern, Neubrückstrasse 10, CH-3012, Bern, Switzerland

    X. Jiang & H. Bunke

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  1. X. Jiang
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  2. H. Bunke
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Jiang, X., Bunke, H. On the coding of ordered graphs. Computing 61, 23–38 (1998). https://doi.org/10.1007/BF02684448

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  • DOI: https://doi.org/10.1007/BF02684448

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