Near Linear Time Construction of an Approximate Index for All Maximum Consecutive Sub-sums of a Sequence

  • Ferdinando Cicalese
  • Eduardo Laber
  • Oren Weimann
  • Raphael Yuster
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7354)


We present a novel approach for computing all maximum consecutive subsums in a sequence of positive integers in near linear time. Solutions for this problem over binary sequences can be used for reporting existence (and possibly one occurrence) of Parikh vectors in a bit string. Recently, several attempts have been tried to build indexes for all Parikh vectors of a binary string in subquadratic time. However, to the best of our knowledge, no algorithm is know to date which can beat by more than a polylogarithmic factor the natural Θ(n 2) exhaustive procedure. Our result implies an approximate construction of an index for all Parikh vectors of a binary string in O(n 1 + η ) time, for any constant η > 0. Such index is approximate, in the sense that it leaves a small chance for false positives, i.e., Parikh vectors might be reported which are not actually present in the string. No false negative is possible. However, we can tune the parameters of the algorithm so that we can strictly control such a chance of error while still guaranteeing strong sub-quadratic running time.


Parikh vectors maximum subsequence sum approximate pattern matching approximation algorithms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ferdinando Cicalese
    • 1
  • Eduardo Laber
    • 2
  • Oren Weimann
    • 3
  • Raphael Yuster
    • 4
  1. 1.Department of Computer ScienceUniversity of SalernoItaly
  2. 2.Department of InformaticsPUC-RioRio de JaneiroBrazil
  3. 3.Department of Computer ScienceUniversity of HaifaIsrael
  4. 4.Department of MathematicsUniversity of HaifaIsrael

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