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International Symposium on String Processing and Information Retrieval

SPIRE 2010: String Processing and Information Retrieval pp 270–278Cite as

On Shortest Common Superstring and Swap Permutations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6393))

Abstract

The Shortest Common Superstring (SCS) is a well studied problem, having a wide range of applications. In this paper we consider two problems closely related to it. First we define the Swapped Restricted Superstring(SRS) problem, where we are given a set S of n strings, s 1, s 2, ..., s n , and a text T = t 1 t 2 ...t m , and our goal is to find a swap permutation π: {1, ..., m} →{1, ..., m} to maximize the number of strings in S that are substrings of t π(1) t π(2)...t π(m). We then show that the SRS problem is NP-Complete. Afterwards, we consider a similar variant denoted SRSR, where our goal is to find a swap permutation π: {1, ..., m} →{1, ..., m} to maximize the total number of times that the strings of S appear in t π(1) t π(2)...t π(m) (we can count the same string s i as a substring of t π(1) t π(2)...t π(m) more than once). For this problem, we present a polynomial time exact algorithm.

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References

  1. Amir, A., Aumann, Y., Landau, G.M., Lewenstein, M., Lewenstein, N.: Pattern matching with swaps. J. Algorithms 37(2), 247–266 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Amir, A., Eisenberg, E., Porat, E.: Swap and mismatch edit distance. Algorithmica 45(1), 109–120 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Amir, A., Landau, G.M., Lewenstein, M., Lewenstein, N.: Efficient special cases of pattern matching with swaps. Inf. Process. Lett. 68(3), 125–132 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Amir, A., Lewenstein, M., Porat, E.: Approximate swapped matching. Inf. Process. Lett. 83(1), 33–39 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Antoniou, P., Iliopoulos, C.S., Jayasekera, I., Sohel Rahman, M.: Implementation of a swap matching algorithm using a graph theoretic model. In: BIRD, pp. 446–455 (2008)

    Google Scholar 

  6. Ardila, Y.J.P., Iliopoulos, C.S., Landau, G.M., Mohamed, M.: Approximation algorithm for the cyclic swap problem. In: Stringology, pp. 190–200 (2005)

    Google Scholar 

  7. Blum, A., Jiang, T., Li, M., Tromp, J., Yannakakis, M.: Linear approximation of shortest superstrings. J. ACM 41(4), 630–647 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  8. Clifford, R., Gotthilf, Z., Lewenstein, M., Popa, A.: Restricted common superstring and restricted common supersequence. CoRR, abs/1004.0424v2 (2010)

    Google Scholar 

  9. Garey, M.R., Johnson, D.S.: Computers and intractability. A guide to the theory of NP-completeness. W. H. Freeman, New York (1979)

    MATH  Google Scholar 

  10. Hori, H., Shimozono, S., Takeda, M., Shinohara, A.: Fragmentary pattern matching: Complexity, algorithms and applications for analyzing classic literary works. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, pp. 719–730. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Iliopoulos, C.S., Sohel Rahman, M.: A new model to solve the swap matching problem and efficient algorithms for short patterns. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 316–327. Springer, Heidelberg (2008)

    Google Scholar 

  12. Kaplan, H., Lewenstein, M., Shafrir, N., Sviridenko, M.: Approximation algorithms for asymmetric tsp by decomposing directed regular multigraphs. J. ACM 52(4), 602–626 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Knuth, D.E., Morris Jr., J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM J. Comput. 6(2), 323–350 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ott, S.: Lower bounds for approximating shortest superstrings over an alphabet of size 2. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds.) WG 1999. LNCS, vol. 1665, pp. 55–64. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  15. Sacerdoti, E.D.: A structure for plans and behavior. American Elsevier (1977)

    Google Scholar 

  16. Sweedyk, Z.: A 2\(\frac{1}{2}\)-approximation algorithm for shortest superstring. SIAM J. Comput. 29(3), 954–986 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  17. Tate, A.: Generating project networks. In: IJCAI, pp. 888–893 (1977)

    Google Scholar 

  18. Ukkonen, E.: On-line construction of suffix trees. Algorithmica 14(3), 249–260 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wilkins, D.E.: Practical planning: Extending the classical ai planning paradigm. Morgan Kaufmann, CA (1988)

    Google Scholar 

  20. Zhang, H., Guo, Q., Iliopoulos, C.S.: String matching with swaps in a weighted sequence. In: Zhang, J., He, J.-H., Fu, Y. (eds.) CIS 2004. LNCS, vol. 3314, pp. 698–704. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, Ramat Gan, 52900, Israel

    Zvi Gotthilf & Moshe Lewenstein

  2. Department of Computer Science, University of Bristol, UK

    Alexandru Popa

Authors
  1. Zvi Gotthilf
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  2. Moshe Lewenstein
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  3. Alexandru Popa
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Editor information

Editors and Affiliations

  1. School of Physics and Mathematics, Edificio "B", Universidad Michoacana, Ciudad Universitaria, 5800, Morelia, Mich., Mexico

    Edgar Chavez

  2. Dept. of Computer Science and Enginerring, University of California, 92521, Riverside, CA, USA

    Stefano Lonardi

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Gotthilf, Z., Lewenstein, M., Popa, A. (2010). On Shortest Common Superstring and Swap Permutations. In: Chavez, E., Lonardi, S. (eds) String Processing and Information Retrieval. SPIRE 2010. Lecture Notes in Computer Science, vol 6393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16321-0_28

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  • DOI: https://doi.org/10.1007/978-3-642-16321-0_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16320-3

  • Online ISBN: 978-3-642-16321-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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