Abstract
We consider efficient ways of analyzing families of hierarchical engineering designs, using methods from the area of graph grammars. Our approach starts from an equivalent reformulation of hyperedge replacement systems that is particularly well suited for complexity analysis. We define a characteristic called ”finiteness” of graph properties and give a combinatorial decision algorithm for deciding whether a graph language generated by a given cellular graph grammar has a graph with a given finite graph property. We introduce structural parameters that bound the complexity of the decision procedure and discuss special cases for which the decision can be made in polynomial time. Extensions to non context-free graph grammars are also given. Our results provide explicit and efficient combinatorial algorithms solving problems whose decidability has been proved in a general framework by Courcelle.
(Extended Abstract)
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
A. Arnborg, J. Lagergren, D. Seese, ”Which problems are easy for tree-decomposable graphs?” to appear in Proceedings of ICALP '88, Springer Lecture Notes in Computer Science (1988)
M.W. Bern, E.L. Lawler, A.L. Wong, ”Linear-time computation of optimal subgraphs of decomposable graphs,” Journal of Algorithms Vol. 8, pp. 216–235 (1987)
F.J. Brandenburg, ”On polynomial time graph grammars,” Proceedings of STACS '88 (R. Cori, M.Wirsing, eds.), Springer Lecture Notes in Computer Science No. 294, pp. 227–236 (1988)
B. Courcelle, Recognizability and monadic second order definability for sets of finite graphs, Research report 8634 Bordeaux I University (1986). Submitted for publication.
B. Courcelle, ”On context-free sets of graphs and their monadic second order theory,” Graph-Grammars and Their Application to Computer Science (H. Ehrig, A. Rosenfeld, G. Rozenberg, eds.), Springer Lecture Notes in Computer Science No. 291, pp. 133–146 (1987)
B. Courcelle, ”An axiomatic definition of context-free rewriting and its application to NLC graph grammars,” Proceedings of STACS '88 (R. Cori, M.Wirsing, eds.), Springer Lecture Notes in Computer Science No. 294, pp. 237–247 (1988)
H. Galperin, Succinct representation of graphs, Ph.D. Thesis, Department of EECS Princeton University, Princeton N.J. (1982)
A. Habel, H.J. Kreowski, ”May we introduce to you: Hypergraph Languages Generated by Edge Replacement,” Graph-Grammars and Their Application to Computer Science (H. Ehrig, A. Rosenfeld, G. Rozenberg, eds.), Springer Lecture Notes in Computer Science No. 291 (1987)
A. Habel, H.J. Kreowski, ”Some structural aspects of hypergraph languages generated by hyperedge replacement,” Proceedings of STACS '87 (F.J. Brandenburg, G. Vidal-Naquet, M. Wirsing, eds.), Springer Lecture Notes in Computer Science No. 247, pp. 207–219 (1987)
K. Iwona, K. Steiglitz, ”Testing for cycles in infinite graphs with periodic structure,” Proceedings of 19th ACM STOC, pp. 46–55 (1987)
D. Janssens, G. Rozenberg, ”Decision problems for node label controlled graph grammars,” Journal of Computer and System Sciences Vol. 22, pp. 144–177 (1981)
C. Lautemann, ”Efficient algorithms on context-free graph languages,” to appear in Proceedings of ICALP '88, Springer Lecture Notes in Computer Science (1988)
T. Lengauer, ”Hierarchical planarity testing algorithms,” Proceedings of ICALP '86 (L. Kott, ed.), Springer Lecture Notes in Computer Science No. 226, pp. 215–225 (1986)
T. Lengauer, ”Efficient algorithms for finding minimum spanning forests of hierarchically defined graphs,” Journal of Algorithms Vol. 8, pp. 260–284 (1987)
T. Lengauer, K.W. Wagner, ”The correlation between the complexities of the non-hierarchical and hierarchical version of graph problems,” Proceedings of STACS '87 (F.J. Brandenburg, G. Vidal-Naquet, M. Wirsing, eds.), Springer Lecture Notes in Computer Science No. 247, pp. 100–113 (1987)
T. Lengauer, E. Wanke, ”Efficient solution of connectivity problems on hierarchically defined graphs,” to appear in SIAM Journal of Computing (1988)
T. Lengauer, E. Wanke, Efficient analysis of graph properties on context-free graph languages, Universität-GH Paderborn Fachbereich 17, Informatik Bericht No. 45 (1987)
J.Y.-T. Leung, O. Vornberger, J. Witthof, ”On some variations of the bandwidth minimization problem,” SIAM Journal of Computing Vol. 13, pp. 650–667 (1984)
M.G. Main, G. Rozenberg, ”Edge-label controlled graph grammars,” Graph-Grammars and Their Application to Computer Science (H. Ehrig, A. Rosenfeld, G. Rozenberg, eds.), Springer Lecture Notes in Computer Science No. 291 (1987)
G. Rozenberg, E. Welzl, ”Boundary NLC graph grammars — basic definitions, normal forms, and complexity,” Information and Control Vol. 69, pp. 136–167 (1986)
G. Rozenberg, E. Welzl, ”Graph theoretic closure properties of the family of boundary NLC graph languages,” Acta Informatica Vol. 23, pp. 289–309 (1986)
G. Rozenberg, personal communication.
A.O. Slisenko, ”Context-free grammars as a tool for describing polynomial-time subciasses of hard problems,” Information Processing Letters Vol. 14, pp. 52–56 (1982)
K. Takamizawa, T. Nishizeki, N. Saito, ”Linear-time computability of combinatorial problems on series-parallel graphs,” Journal of the ACM Vol. 29, No. 3, pp. 623–641 (1982)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lengauer, T., Wanke, E. (1988). Efficient analysis of graph properties on context-free graph languages. In: Lepistö, T., Salomaa, A. (eds) Automata, Languages and Programming. ICALP 1988. Lecture Notes in Computer Science, vol 317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19488-6_129
Download citation
DOI: https://doi.org/10.1007/3-540-19488-6_129
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19488-0
Online ISBN: 978-3-540-39291-0
eBook Packages: Springer Book Archive