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International Symposium on String Processing and Information Retrieval

SPIRE 2018: String Processing and Information Retrieval pp 311–324Cite as

Linear-Time Online Algorithm Inferring the Shortest Path from a Walk

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11147))

Abstract

We consider the problem of inferring an edge-labeled graph from the sequence of edge labels seen in a walk of that graph. It has been known that this problem is solvable in \(\mathrm {O}(n \log n)\) time when the targets are path or cycle graphs. This paper presents an online algorithm for the problem of this restricted case that runs in \(\mathrm {O}(n)\) time, based on Manacher’s algorithm for computing all the maximal palindromes in a string.

S. Narisada—Currently affiliated with KDDI Corporation, Tokyo, Japan.

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Notes

  1. 1.

    To avoid lengthy expressions, we casually say that a palindrome centered at c in x becomes or grows to a bigger palindrome in xy when \(\rho _x(c) < \rho _{xy}(c)\), without explicitly mentioning several involved mathematical objects that should be understood from the context or that are not important. Other similar phrases should be understood in an appropriate way.

References

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  2. Aslam, J.A., Rivest, R.L.: Inferring graphs from walks. In: Computational Learning Theory, pp. 359–370 (1990)

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  3. Manacher, G.K.: A new linear-time on-line algorithm for finding the smallest initial palindrome of a string. J. ACM 22(3), 346–351 (1975)

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Acknowledgments

The research is supported by JSPS KAKENHI Grant Numbers JP15H05706, JP26330013 and JP18K11150, and ImPACT Program of Council for Science, Technology and Innovation (Cabinet Office, Government of Japan).

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Sendai, Japan

    Shintaro Narisada, Diptarama Hendrian, Ryo Yoshinaka & Ayumi Shinohara

Authors
  1. Shintaro Narisada
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  2. Diptarama Hendrian
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  3. Ryo Yoshinaka
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  4. Ayumi Shinohara
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Corresponding author

Correspondence to Ryo Yoshinaka .

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Editors and Affiliations

  1. Diego Portales University, Santiago, Chile

    Travis Gagie

  2. The University of Melbourne, Melbourne, VIC, Australia

    Alistair Moffat

  3. University of Chile, Santiago, Chile

    Gonzalo Navarro

  4. Universidad de Ingeniería y Tecnología, Lima, Peru

    Ernesto Cuadros-Vargas

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Narisada, S., Hendrian, D., Yoshinaka, R., Shinohara, A. (2018). Linear-Time Online Algorithm Inferring the Shortest Path from a Walk. In: Gagie, T., Moffat, A., Navarro, G., Cuadros-Vargas, E. (eds) String Processing and Information Retrieval. SPIRE 2018. Lecture Notes in Computer Science(), vol 11147. Springer, Cham. https://doi.org/10.1007/978-3-030-00479-8_25

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  • DOI: https://doi.org/10.1007/978-3-030-00479-8_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00478-1

  • Online ISBN: 978-3-030-00479-8

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