Sub-quadratic time and linear space data structures for permutation matching in binary strings

  • Authors:
  • Tanaeem M. Moosa;M. Sohel Rahman

  • Affiliations:
  • AEDA Group, Department of CSE, BUET, Dhaka-1000, Bangladesh;AEDA Group, Department of CSE, BUET, Dhaka-1000, Bangladesh

  • Venue:
  • Journal of Discrete Algorithms
  • Year:
  • 2012

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Abstract

Given a pattern P of length n and a text T of length m, the permutation matching problem asks whether any permutation of P occurs in T. Indexing a string for permutation matching seems to be quite hard in spite of the existence of a simple non-indexed solution. In this paper, we devise several o(n^2) time data structures for a binary string capable of answering permutation queries in O(m) time. In particular, we first present two O(n^2/logn) time data structures and then improve the data structure construction time to O(n^2/log^2n). The space complexity of the data structures remains linear.