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Finding Missing Patterns

  • Shunsuke Inenaga
  • Teemu Kivioja
  • Veli Mäkinen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3240)

Abstract

Consider the following problem: Find the shortest pattern that does not occur in a given text. To make the problem non-trivial, the pattern is required to consist only of characters that occur in the text. This problem can be solved easily in linear time using the suffix tree of the text. In this paper, we study an extension of this problem, namely the missing patterns problem: Find the shortest pair of patterns that do not occur close to each other in a given text, i.e., the distance between their occurrences is always greater than a given threshold α. We show that the missing patterns problem can be solved in O( min (αnlogn,n 2)) time, where n is the size of the text. For the special case where both pairs are required to have the same length, we give an algorithm with time complexity O(αn log log n). The problem is motivated by optimization of multiplexed nested-PCR.

Keywords

Multiplex Polymerase Chain Reaction Nest Polymerase Chain Reaction Pattern Problem Pattern Pair Biological Motivation 
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 2004

Authors and Affiliations

  • Shunsuke Inenaga
    • 1
  • Teemu Kivioja
    • 1
  • Veli Mäkinen
    • 1
  1. 1.Department of Computer ScienceUniversity of HelsinkiFinland

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