Self-normalised distance with don't cares

  • Authors:

  • Peter Clifford;Raphaël Clifford

  • Affiliations:

  • Dept. of Statistics, University of Oxford, UK;Dept. of Computer Science, University of Bristol, Bristol, UK

  • Venue:
  • CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
  • Year:
  • 2007

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Abstract

We present O(n logm) algorithms for a new class of problems termed self-normalised distance with don't cares. The input is a pattern p of length m and text t of length n m. The elements of these strings are either integers or wild card symbols. In the shift version, the problem is to compute minaα Σj=0m-1 (α + pj - ti+j)2 for all i, where wild cards do not contribute to the sum. In the shift-scale version, the objective is to compute minα,β Σj=0m-1 (α + βpj - ti+j)2 for all i, similarly. We show that the algorithms have the additional benefit of providing simple O(n logm) solutions for the problems of exact matching with don't cares, exact shift matching with don't cares and exact shift-scale matching with don't cares.