Algorithms for approximate string matching
Information and Control
Fast string matching with k-differences
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Alphabet dependence in parameterized matching
Information Processing Letters
SIAM Journal on Computing
Suffix arrays: a new method for on-line string searches
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
A sub-quadratic sequence alignment algorithm for unrestricted cost matrices
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Information and Computation
Fast on-line integer multiplication
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Swap and mismatch edit distance
Algorithmica
A Black Box for Online Approximate Pattern Matching
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Pattern matching with address errors: Rearrangement distances
Journal of Computer and System Sciences
Self-normalised distance with don't cares
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Lower bounds for online integer multiplication and convolution in the cell-probe model
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Pattern matching in multiple streams
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
A simple pattern matching algorithm for weighted sequences
Proceedings of the 2012 ACM Research in Applied Computation Symposium
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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 @?"j@D(P[j],T[i+j]), where @D is any distance function between individual characters. We show in this work how to tackle online approximate matching when the distance function is non-local. We give new 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 and L"1 and L"2 rearrangement distances. The resulting online algorithms bound the worst case running time per input character to within a log factor of their comparable offline counterpart.