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.
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Clifford, R., Sach, B. (2009). Online Approximate Matching with Non-local Distances. In: Kucherov, G., Ukkonen, E. (eds) Combinatorial Pattern Matching. CPM 2009. Lecture Notes in Computer Science, vol 5577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02441-2_13
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DOI: https://doi.org/10.1007/978-3-642-02441-2_13
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