Algorithms for Computing the λ-regularities in Strings

  • Authors:
  • Hui Zhang;Qing Guo;Costas S. Iliopoulos

  • Affiliations:
  • College of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou Zhejiang 310018, China. E-mail: hzvicky@gmail.com;Department of Computer Science and Engineering, Zhejiang University Hangzhou Zhejiang 310027, China. E-mail: guoqing@tiansign.com;Department of Computer Science, King's College London Strand, London WC2R 2LS, England. E-mail: csi@dcs.kcl.ac.uk

  • Venue:
  • Fundamenta Informaticae - Workshop on Combinatorial Algorithms
  • Year:
  • 2008

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Abstract

We introduce the notion of λ-regularities in strings that consist of λ-covers and λ-seeds, and study three λ-regularities problems - the λ-cover problem, the general λ-cover problem and the λ-seed problem in this paper. λ-regularities can be viewed as generalized string regularities in the sense that a set of λ repetitive strings rather than a single repeated string are considered. We first present a general algorithm for computing all the λ-combinations of a given string, since they serve as candidates for both λ-covers and λ-seeds. The running time of this algorithm is O(n$^2$). Relying on this result, we answer the above mentioned three problems all in O(n$^2$) time.