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Pattern matching in directed graphs

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Book cover Combinatorial Pattern Matching (CPM 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 937))

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Abstract

Pattern matching in directed graphs is a natural extension of pattern matching in trees and has many applications to different areas. In this paper, we study several pattern matching problems in ordered labeled directed graphs. For the rooted directed graph pattern matching problem, we present an efficient algorithm which runs in time and space O(¦E(P)¦×¦V(T)¦+¦E(T)¦), where ¦E(P)¦, ¦V(T)¦ and ¦E(T)¦ are the number of edges in the pattern graph P, the number of nodes in the target graph T and the number of edges in the pattern graph T, respectively. It is by far the fastest algorithm for this problem. This algorithm can also solve the directed graph pattern matching problem without increasing time or space complexity. Our solution to this problem outperforms the best existing method by Katzenelson, Pinter and Schenfeld by a factor of at least ¦V(P)¦. We also present an algorithm for the directed graph topological embedding problem which runs in time O(¦V(P)¦×¦E(T)¦+¦E(P)¦) and space O(¦V(P)¦×¦V(T)¦+¦E(P)¦+¦E(T)¦), where ¦V(P)¦ is the number of nodes in the pattern graph P. To our knowledge, this algorithm is the first one for this problem.

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References

  1. A.V. Aho, R. Sethi, and J. D. Ullman. Compilers — Principles, Techniques, and Tools, chapter 6.7. Addison Wesley, 1986.

    Google Scholar 

  2. Alexander Aiken and Brian R. Murphy. Implementing regular tree expressions. In Proceedings of 5th ACM Conference on Functional Programming Languages and Computer Architecture, pages 427–447, 1991.

    Google Scholar 

  3. Alexander Aiken and Brian R. Murphy. Static type inference in a dynamically typed language. In Proceedings of Eighteenth Annual ACM Symposium on Principles of Programming Languages, pages 279–290, 1991.

    Google Scholar 

  4. S. A. Cook. The complexity of theorem-proving procedures. In Proceedings of the 3rd Annual Symposium on the Theory of Computing, pages 151–158, 1971.

    Google Scholar 

  5. Andrea Corradini. Term rewriting in 77-01. In Proceedings of International Joint Conference on Theory and Practice of Software Development, pages 468–484, 1993.

    Google Scholar 

  6. Nachum Dershowitz and Stéphane Kaplan. Rewrite, rewrite, rewrite, rewrite, rewrite ... In Proceedings of Sixteenth Annual Symposium on Principles of Programming Languages, pages 250–259, 1989.

    Google Scholar 

  7. J. R. W. Glauert, J. R. Kennaway, and M. R. Sleep. Dactl: An experimental graph rewriting language. In Proceedings of Fourth International Workshop on Graph Grammars and Their Application to Computer Science, pages 378–395, 1990.

    Google Scholar 

  8. N. Heintze and J. Jaffar. A finite presentation theorem for approximating logic programs. In Proceedings of Seventeenth Annual ACM Symposium on Principles of Programming Languages, pages 197–209, 1990.

    Google Scholar 

  9. Christoph M. Hoffmann and Michael J. O'Donnell. Pattern matching in trees. Journal of ACM, 29(1):68–95, 1982.

    Article  Google Scholar 

  10. Kristoffer H. Holm. Graph matching in operational semantics and typing. In Proceedings of Colloquium on Trees in Algebra and Programming, pages 191–205, 1990.

    Google Scholar 

  11. Jacob Katzenelson, Shlomit S. Pinter, and Eugen Schenfeld. Type matching, type-graphs, and the Schanuel conjecture. ACM Transactions on Programming Languages and Systems, 14(4):574–588, Oct. 1992.

    Google Scholar 

  12. Jan Willem Klop. Term rewriting systems. Technical Report CS-R9073, Free University, Department of Mathematics and Computer Science, 1990.

    Google Scholar 

  13. R. Tarjan. Depth first search and linear graph algorithms. SIAM Journal on Computing, 1(2):146–160, 1972.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, ON, Canada

    Jianghai Fu

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  1. Jianghai Fu
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Zvi Galil Esko Ukkonen

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© 1995 Springer-Verlag Berlin Heidelberg

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Fu, J. (1995). Pattern matching in directed graphs. In: Galil, Z., Ukkonen, E. (eds) Combinatorial Pattern Matching. CPM 1995. Lecture Notes in Computer Science, vol 937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60044-2_35

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  • DOI: https://doi.org/10.1007/3-540-60044-2_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60044-2

  • Online ISBN: 978-3-540-49412-6

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