Computing Equality-Free String Factorisations

  • Markus L. SchmidEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9136)


A factorisation of a string is equality-free if each two factors are different; its size is the number of factors and its width is the maximum length of any factor. To decide, for a string \(w\) and a number \(m\), whether \(w\) has an equality-free factorisation with a size of at least (or a width of at most) \(m\) are \(\mathrm {NP}\)-complete problems. We further investigate the complexity of these problems and also study the converse problems of computing a factorisation that is to a large extent not equality-free, i.e., a factorisation of size at least (or width at most) \(m\) such that the total number of different factors does not exceed a given bound \(k\).


String factorisations \(\mathrm {NP}\)-hard string problems FPT 


  1. 1.
    Bulteau, L., Hüffner, F., Komusiewicz, C., Niedermeier, R.: Multivariate algorithmics for NP-hard string problems. EATCS Bull. 114, 31–73 (2014)Google Scholar
  2. 2.
    Condon, A., Maňuch, J., Thachuk, C.: Complexity of a collision-aware string partition problem and its relation to oligo design for gene synthesis. In: Hu, X., Wang, J. (eds.) COCOON 2008. LNCS, vol. 5092, pp. 265–275. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  3. 3.
    Condon, A., Maňuch, J., Thachuk, C.: The complexity of string partitioning. In: Kärkkäinen, J., Stoye, J. (eds.) CPM 2012. LNCS, vol. 7354, pp. 159–172. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  4. 4.
    Fernau, H., Manea, F., Mercaş, R., Schmid, M.L.: Pattern matching with variables: fast algorithms and new hardness results. In: Leibniz International Proceedings in Informatics (LIPIcs), Proceedings 32nd Symposium on Theoretical Aspects of Computer Science, STACS 2015, vol. 30, pp. 302–315 (2015)Google Scholar
  5. 5.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, New York (2006)Google Scholar
  6. 6.
    Gagie, T., Inenaga, S., Karkkainen, J., Kempa, D., Piatkowski, M., Puglisi, S.J., Sugimoto, S.: Diverse palindromic factorization is NP-complete. Technical report 1503.04045 (2015).
  7. 7.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. W.H. Freeman and Company, San Francisco (1979) zbMATHGoogle Scholar
  8. 8.
    Jiang, H., Su, B., Xiao, M., Xu, Y., Zhong, F., Zhu, B.: On the exact block cover problem. In: Gu, Q., Hell, P., Yang, B. (eds.) AAIM 2014. LNCS, vol. 8546, pp. 13–22. Springer, Heidelberg (2014) Google Scholar
  9. 9.
    Knuth, D.E., Morris, J.H., Pratt, V.R.: Fast pattern matching in strings. Commun. ACM 6(2), 323–350 (1977)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Fachbereich IV – Abteilung InformatikwissenschaftenUniversität TrierTrierGermany

Personalised recommendations