Pseudo-realtime pattern matching: closing the gap

  • Authors:

  • Raphaël Clifford;Benjamin Sach

  • Affiliations:

  • Department of Computer Science, University of Bristol, UK;Department of Computer Science, University of Bristol, UK

  • Venue:
  • CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
  • Year:
  • 2010

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Abstract

We consider the k-difference and k-mismatch problems in the pseudo-realtime model where the text arrives online and the time complexity measure is per arriving character and unamortised. The well-known k-difference/k-mismatch problems are those of finding all alignments of a pattern of length m with a text of length n where the edit/Hamming distance is at most k. Offline, the literature gives efficient solutions in O(nk) and O(n√k log k) time, respectively. More recently, a pseudo-realtime solution was given for the former in O(k log m) time and the latter in O(√k log k log m) time per arriving text character. Our work improves these complexities to O(k) time for the k-difference problem and O(√k log k +log m) for the k-mismatch problem. In the process of developing the main results, we also give a simple solution with optimal time complexity for performing longest common extension queries in the same pseudo-realtime setting which may be of independent interest.