Abstract
In this paper, as a variation of a Tai mapping between trees, we introduce a segmental mapping to preserve the parent-children relationship as possible. Then, we show that the segmental mapping provides a new hierarchy for the classes of Tai mappings in addition to a well-known one. Also we show that the segmental distance as the minimum cost of segmental mappings is a metric. Finally, we design the algorithm to compute the segmental distance in quadratic time and space.
This work is partially supported by Grand-in-Aid for Scientific Research 22240010, 24240021 and 24300060 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Chawathe, S.S.: Comparing hierarchical data in external memory. In: Proc. VLDB 1999, pp. 90–101 (1999)
Demaine, E.D., Mozes, S., Rossman, B., Weimann, O.: An optimal decomposition algorithm for tree edit distance. ACM Trans. Algorithms 6 (2009)
Kuboyama, T.: Matching and learning in trees. Ph.D thesis, University of Tokyo (2007), http://tk.cc.gakushuin.ac.jp/doc/kuboyama2007phd.pdf
Selkow, S.M.: The tree-to-tree editing problem. Inform. Process. Lett. 6, 184–186 (1977)
Tai, K.-C.: The tree-to-tree correction problem. J. ACM 26, 422–433 (1979)
Valiente, G.: An efficient bottom-up distance between trees. In: Proc. SPIRE 2001, pp. 212–219 (2001)
Wang, J.T.L., Zhang, K.: Finding similar consensus between trees: An algorithm and a distance hierarchy. Pattern Recog. 34, 127–137 (2001)
Yamamoto, Y., Hirata, K., Kuboyama, T.: A bottom-up edit distance between rooted labeled trees. In: Proc. LLLL 2011, pp. 26–33 (2011)
Zhang, K.: Algorithms for the constrained editing distance between ordered labeled trees and related problems. Pattern Recog. 28, 463–474 (1995)
Zhang, K., Wang, J.T.L., Shasha, D.: On the editing distance between undirected acyclic graph. Int. J. Found. Comput. Sci. 7, 43–58 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kan, T., Higuchi, S., Hirata, K. (2012). Segmental Mapping and Distance for Rooted Labeled Ordered Trees. In: Chao, KM., Hsu, Ts., Lee, DT. (eds) Algorithms and Computation. ISAAC 2012. Lecture Notes in Computer Science, vol 7676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35261-4_51
Download citation
DOI: https://doi.org/10.1007/978-3-642-35261-4_51
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35260-7
Online ISBN: 978-3-642-35261-4
eBook Packages: Computer ScienceComputer Science (R0)