Extreme Witnesses and Their Applications

  • Andrzej Lingas
  • Mia Persson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9486)


We study the problem of computing the so called minimum and maximum witnesses for Boolean vector convolution. We also consider a generalization of the problem which is to determine for each positive coordinate of the convolution vector, q smallest (or, largest) witnesses, where q is the minimum of a parameter k and the number of witnesses for this coordinate. We term this problem the smallest k-witness problem or the largest k-witness problem, respectively. We also study the corresponding smallest and largest k-witness problems for Boolean matrix product. In both cases, we provide algorithmic solutions and applications to the aforementioned witness problems, among other things in string matching and computing the \((\min , +)\) vector convolution.


Boolean vector convolution Boolean matrix product String matching Witnesses Minimum and maximum witnesses Time complexity Lightest triangles 



We thank Mirosław Kowaluk for valuable comments.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceLund UniversityLundSweden
  2. 2.Department of Computer ScienceMalmö UniversityMalmöSweden

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