Online Approximate Matching with Non-local Distances

  • Authors:

  • Raphaël Clifford;Benjamin Sach

  • Affiliations:

  • Dept. of Computer Science, University of Bristol, Bristol, UK BS8 1UB;Dept. of Computer Science, University of Bristol, Bristol, UK BS8 1UB

  • Venue:
  • CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
  • Year:
  • 2009

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Abstract

A black box method was recently given that solves the problem of online approximate matching for a class of problems whose distance functions can be classified as being local. A distance function is said to be local if for a pattern P of length m and any substring T [i ,i + m *** 1] of a text T , the distance between P and T [i ,i + m *** 1] is equal to Σ j Δ (P [j ], T [i + j *** 1]), where Δ is any distance function between individual characters. We extend this line of work by showing how to tackle online approximate matching when the distance function is non-local. We give solutions which are applicable to a wide variety of matching problems including function and parameterised matching, swap matching, swap-mismatch, k -difference, k -difference with transpositions, overlap matching, edit distance/LCS, flipped bit, faulty bit and L 1 and L 2 rearrangement distances. The resulting unamortised online algorithms bound the worst case running time per input character to within a log factor of their comparable offline counterpart.