Abstract
This paper introduces a new problem of inferring strings from graphs, and inferring strings from arrays. Given a graph G or an array A, we infer a string that suits the graph, or the array, under some condition. Firstly, we solve the problem of finding a string w such that the directed acyclic subsequence graph (DASG) of w is isomorphic to a given graph G. Secondly, we consider directed acyclic word graphs (DAWGs) in terms of string inference. Finally, we consider the problem of finding a string w of a minimal size alphabet, such that the suffix array (SA) of w is identical to a given permutation p=p 1,...,p n of integers 1,...,n. Each of our three algorithms solving the above problems runs in linear time with respect to the input size.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Crochemore, M., Rytter, W.: Jewels of Stringology. World Scientific, Singapore (2002)
Baeza-Yates, R.A.: Searching subsequences (note). Theoretical Computer Science 78, 363–376 (1991)
Blumer, A., Blumer, J., Haussler, D., Ehrenfeucht, A., Chen, M.T., Seiferas, J.: The smallest automaton recognizing the subwords of a text. Theoretical Computer Science 40, 31–55 (1985)
Franěk, F., Gao, S., Lu, W., Ryan, P.J., Smyth, W.F., Sun, Y., Yang, L.: Verifying a border array in linear time. J. Comb. Math. Comb. Comput., 223–236 (2002)
Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The design and analysis of computer algorithms. Addison-Wesley, Reading (1974)
Duval, J.P., Lecroq, T., Lefevre, A.: Border array on bounded alphabet. In: Proc. The Prague Stringology Conference 2002 (PSC 2002), pp. 28–35. Czech Technical University (2002)
Manber, U., Myers, G.: Suffix arrays: A new method for on-line string searches. SIAM J. Compt. 22, 935–948 (1993)
Atallah, M.J. (ed.): Algorithms and Theory of Computation Handbook. CRC Press, Boca Raton (1998) ISBN:0-8493-2649-4
Crochemore, M.: Transducers and repetitions. Theoretical Computer Science 45, 63–86 (1986)
Graham, R., Knuth, D., Patashnik, O.: Concrete Mathematics, 2nd edn. Addison Wesley, Reading (1994)
Allauzen, C., Crochemore, M., Raffinot, M.: Factor oracle: A new structure for pattern matching. In: Bartosek, M., Tel, G., Pavelka, J. (eds.) SOFSEM 1999. LNCS, vol. 1725, pp. 291–306. Springer, Heidelberg (1999)
Weiner, P.: Linear pattern matching algorithms. In: Proc. 14th Annual Symposium on Switching and Automata Theory, pp. 1–11 (1973)
Blumer, A., Blumer, J., Haussler, D., McConnell, R., Ehrenfeucht, A.: Complete inverted files for efficient text retrieval and analysis. Journal of the ACM 34, 578–595 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bannai, H., Inenaga, S., Shinohara, A., Takeda, M. (2003). Inferring Strings from Graphs and Arrays. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-45138-9_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40671-6
Online ISBN: 978-3-540-45138-9
eBook Packages: Springer Book Archive