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Faster Algorithm for the Set Variant of the String Barcoding Problem

  • Leszek Gąsieniec
  • Cindy Y. Li
  • Meng Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5029)

Abstract

A string barcoding problem is defined as to find a minimum set of substrings that distinguish between all strings in a given set of strings \({\cal S}\). In a biological sense the given strings represent a set of genomic sequences and the substrings serve as probes in a hybridisation experiment. In this paper, we study a variant of the string barcoding problem in which the substrings have to be chosen from a particular set of substrings of cardinality n. This variant can be also obtained from more general test set problem, see, e.g., [1] by fixing appropriate parameters. We present almost optimal \(O(n|{\cal S}|\log^3 n)\)-time approximation algorithm for the considered problem. Our approximation procedure is a modification of the algorithm due to Berman et al. [1] which obtains the best possible approximation ratio (1 + ln n), providing \(NP\not\subseteq DTIME(n^{\log\log n})\). The improved time complexity is a direct consequence of more careful management of processed sets, use of several specialised graph and string data structures as well as tighter time complexity analysis based on an amortised argument.

Keywords

Equivalence Class Time Complexity Equivalence Relation Span Tree Approximation Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Leszek Gąsieniec
    • 1
  • Cindy Y. Li
    • 2
  • Meng Zhang
    • 3
  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK
  2. 2.Histocompatibility and Immunogenetics LaboratoryNational Blood ServiceBristolUK
  3. 3.College of Computer Science and TechnologyJilin UniversityChangchunChina

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