Pattern matching in pseudo real-time

It has recently been shown how to construct online, non-amortised approximate pattern matching algorithms for a class of problems whose distance functions can be classified as being local. Informally, 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] can be expressed as Σj∆(P[j], T[i + j]), where ∆ is any distance function between individual characters. We show in this work how to tackle online approximate matching when the distance function is nonlocal. We give new solutions which are applicable to a wide variety of matching problems including function and parameterised matching, swap matching, swapmismatch, k-difference, k-difference with transpositions, overlap matching, edit distance/LCS and L1 and L2 rearrangement distances. The resulting online algorithms bound the worst case running time per input character to within a log factor of their comparable offline cou...

• Type: Journal
• Year: 2011
• Where: JDA
• Authors: Raphaël Clifford, Benjamin Sach
• Keywords: Comparable Offline Counterpart, Distance Function, JDA 2011, Non-amortised Approximate Pattern