Optimization Letters

, Volume 4, Issue 1, pp 29–36 | Cite as

An efficient string sorting algorithm for weighing matrices of small weight

  • Ilias S. Kotsireas
  • Christos Koukouvinos
  • Panos M. Pardalos
Original Paper


In this paper, we demonstrate that the search for weighing matrices of small weights constructed from two circulants can be viewed as a string sorting problem together with a linear time algorithm to locate common strings in two sorted arrays. We also introduce a sparse encoding of the periodic autocorrelation function vector, based on concepts from Algorithmic Information Theory, also known as Kolmogorov complexity, that allows us to speed up the algorithm considerably. Finally, we use these ideas to find new weighing matrices W(2 · n, 9) constructed from two circulants, for many values of n in the range 100 ≤  n ≤  300. These matrices are given here for the first time. We also discuss briefly a connection with Combinatorial Optimization.


Weighing matrices Algorithm Pattern String sorting Sparse encoding 

Mathematics Subject Classification (2000)

05B20 62K05 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Ilias S. Kotsireas
    • 1
  • Christos Koukouvinos
    • 2
  • Panos M. Pardalos
    • 3
  1. 1.Department of Physics and Computer ScienceWilfrid Laurier UniversityWaterlooCanada
  2. 2.Department of MathematicsNational Technical University of AthensZografou, AthensGreece
  3. 3.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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