Abstract
The minimum all-suffixes directed acyclic word graph (MASDAWG) of a string w has |w| + 1 initial nodes, where the dag induced by all reachable nodes from the k-th initial node conforms with the DAWG of the k-th suffix of w. A new space-economical algorithm for the construction of MASDAWG(w) is presented. The algorithm reads a given string w from right to left, and constructs MASDAWG(w) without suffix links. It performs in time linear in the output size. Furthermore, we introduce the minimum all-suffixes compact DAWG (MASCDAWG). CDAWGts are known to be more space-economical than DAWGs, and thus MASCDAWG(w) requires smaller space than MASDAWG(w). We present an on-line (right-to-left) algorithm to build MASCDAWG(w) without suffix links, whose running time is also linear in its size.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
D. Angluin. Finding patterns common to a set of strings. J. Comput. Sys. Sci., 21:46–62, 1980.
A. Blumer, J. Blumer, D. Haussler, A. Ehrenfeucht, M. T. Chen, and J. Seiferas. The smallest automaton recognizing the subwords of a text. Theoretical Computer Science, 40:31–55, 1985.
A. Blumer, J. Blumer, D. Haussler, R. McConnell, and A. Ehrenfeucht. Complete inverted files for efficient text retrieval and analysis. J. ACM, 34(3):578–595, 1987.
M. Crochemore and W. Rytter. Text Algorithms. Oxford University Press, New York, 1994.
M. Crochemore and R. Vérin. On compact directed acyclic word graphs. In J. Mycielski, G. Rozenberg, and A. Salomaa, editors, Structures in Logic and Computer Science, volume 1261 of Lecture Notes in Computer Science, pages 192–211. Springer-Verlag, 1997.
D. Gusfield. Algorithms on Strings, Trees, and Sequences. Cambridge University Press, New York, 1997.
S. Inenaga, H. Hoshino, A. Shinohara, M. Takeda, S. Arikawa, G. Mauri, and G. Pavesi. On-line construction of compact directed acyclic word graphs. In A. Amir and G. M. Landau, editors, Proc. 12th Annual Symposium on Combinatorial Pattern Matching (CPM’01), volume 2089 of Lecture Notes in Computer Science, pages 169–180. Springer-Verlag, 2001.
S. Inenaga, M. Takeda, A. Shinohara, H. Hoshino, and S. Arikawa. The minimum dawg for all suffixes of a string and its applications. In Proc. 13th Annual Symposium on Combinatorial Pattern Matching (CPM’02), 2002. (to appear).
E. M. McCreight. A space-economical suffix tree construction algorithm. J. ACM, 23(2):262–272, 1976.
D. Revuz. Minimization of acyclic deterministic automata in linear time. Theoretical Computer Science, 92(1):181–189, 1992.
T. Shinohara. Polynomial-time inference of pattern languages and its applications. In Proc. 7th IBM Symp. Math. Found. Comp. Sci., pages 191–209, 1982.
E. Ukkonen. On-line construction of suffix trees. Algorithmica, 14(3):249–260, 1995.
P. Weiner. Linear pattern matching algorithms. In Proc. 14th Annual Symposium on Switching and Automata Theory, pages 1–11, 1973.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Inenaga, S., Shinohara, A., Takeda, M., Bannai, H., Arikawa, S. (2002). Space-Economical Construction of Index Structures for All Suffixes of a String. In: Diks, K., Rytter, W. (eds) Mathematical Foundations of Computer Science 2002. MFCS 2002. Lecture Notes in Computer Science, vol 2420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45687-2_28
Download citation
DOI: https://doi.org/10.1007/3-540-45687-2_28
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44040-6
Online ISBN: 978-3-540-45687-2
eBook Packages: Springer Book Archive