Weighted Shortest Common Supersequence

  • Amihood Amir
  • Zvi Gotthilf
  • B. Riva Shalom
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7024)


The Shortest Common Supersequence (SCS) is the problem of seeking a shortest possible sequence that contains each of the input sequences as a subsequence. In this paper we consider applying the problem to Position Weight Matrices (PWM). The Position Weight Matrix was introduced as a tool to handle a set of sequences that are not identical, yet, have many local similarities. Such a weighted sequence is a ‘statistical image’ of this set where we are given the probability of every symbol’s occurrence at every text location. We consider two possible definitions of SCS on PWM. For the first, we give a polynomial time algorithm, having two input sequences. For the second, we prove \(\cal{NP}\)-hardness.


Input Sequence Partition Problem Input String Position Weight Matrix Text Location 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Amihood Amir
    • 1
    • 2
  • Zvi Gotthilf
    • 1
  • B. Riva Shalom
    • 3
  1. 1.Department of Computer ScienceBar-Ilan UniversityRamat-GanIsrael
  2. 2.Department of Computer ScienceJohns Hopkins UniversityBaltimoreIsrael
  3. 3.Department of Software EngineeringShenkar CollegeRamat-GanIsrael

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