Abstract
A walk of an edge-colored undirected graph G is a path which contains all edges in G. We show an O(n log n) time algorithm for finding the smallest tree from a walk which allows the walk. If the alphabet of colors is fixed, the algorithm runs in O(n) time. Further, we consider the problem of finding the smallest tree from partial walks, where a partial walk of G is a path in G. We prove that the problem turns to be NP-complete. We also show that inferring the smallest linear chain from partial walks is NP-complete, while the problem of inferring the smallest linear chain from a single walk is known to be solvable in polynomial time.
Preview
Unable to display preview. Download preview PDF.
References
Angluin, D.: On the complexity of minimum inference of regular sets. Inform. Contr. 39 (1978) 337–350
Arikawa, S., Kuhara, S., Miyano, S., Shinohara, A., Shinohara, T.:A learning algorithm for elementary formal systems and its experiments on identification of transmembrane domains. Proc. 25th Hawaii International Conference on System Sciences Vol. I (1992) 675–684
Arikawa, S., Kuhara, S., Miyano, S., Mukouchi, Y., Shinohara, A., Shinohara, T.:A machine discovery from amino acid sequences by decision trees over regular patterns, to appear in Proc. Fifth Generation Computer Systems 1992
Aslam, J.A., Rivest, R.L.: Inferring graphs from walks. Proc. 3rd Computational Learning Theory (1990) 359–370
Gallant, J., Maier, D., Storer, J.A.: On finding minimal length superstrings. J. Comput. System Sci. 20 (1980) 50–58
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, San Francisco (1979)
Gold, E.M.: Complexity of automaton identification from given data. Inform. Contr. 37 (1978) 302–320
Huet, G.: Confluent reductions: abstract properties and applications to term rewriting systems. J. Assoc. Comput. Mach. 27 (1980) 797–821
Li, M.: Towards a DNA sequencing theory. Proc. 31st IEEE Symposium on Foundations of Computer Science (1990) 125–134
Raghavan, V.: Bounded degree graph inference from walks. Proc. 4th Computational Learning Theory (1991) 354–366
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maruyama, O., Miyano, S. (1992). Inferring a tree from walks. In: Havel, I.M., Koubek, V. (eds) Mathematical Foundations of Computer Science 1992. MFCS 1992. Lecture Notes in Computer Science, vol 629. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-55808-X_37
Download citation
DOI: https://doi.org/10.1007/3-540-55808-X_37
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55808-8
Online ISBN: 978-3-540-47291-9
eBook Packages: Springer Book Archive