Efficient two-dimensional pattern matching in the presence of errors
Information Sciences: an International Journal
A technique for two-dimensional pattern matching
Communications of the ACM - Special issue: multiprocessing
Fast parallel and serial multidimensional approximate array matching
Theoretical Computer Science
Efficient 2-dimensional approximate matching of non-rectangular figures
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Fast text searching: allowing errors
Communications of the ACM
Fast two-dimensional pattern matching
Information Processing Letters
Text algorithms
Two and higher dimensional pattern matching in optimal expected time
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Efficient string matching: an aid to bibliographic search
Communications of the ACM
A String Matching Algorithm Fast on the Average
Proceedings of the 6th Colloquium, on Automata, Languages and Programming
Fast Two-Dimensional Approximate Pattern Matching
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Similarity in Two-Dimensional Strings
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
Fast and Practical Approximate String Matching
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
Alphabet Independent and Dictionary Scaled Matching
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Analysis of Two-Dimensional Approximate Pattern Matching Algorithms
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
A Rotation Invariant Filter for Two-Dimensional String Matching
CPM '98 Proceedings of the 9th Annual Symposium on Combinatorial Pattern Matching
Mining semantic structures in movies
INAP'04/WLP'04 Proceedings of the 15th international conference on Applications of Declarative Programming and Knowledge Management, and 18th international conference on Workshop on Logic Programming
A largest common d-dimensional subsequence of two d-dimensional strings
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
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We address the problem of approximate string matching in d dimensions, that is, to find a pattern of size md in a text of size nd with at most k md errors (substitutions, insertions and deletions along any dimension). We use a novel and very flexible error model, for which there exists only an algorithm to evaluate the similarity between two elements in two dimensions at O(m4) time. We extend the algorithm to d dimensions, at O(d!m2d) time and O(d!m2d-1) space. We also give the first search algorithm for such model, which is O(d!mdnd) time and O(d!mdnd-1) space. We show how to reduce the space cost to O(d!3dm2d-1) with little time penalty. Finally, we present the first sublinear-time (on average) searching algorithm (i.e. not all text cells are inspected), which is O(knd/md-1) for k m/(d(logσ m- logσ d)))d-1, where σ is the alphabet size. After that error level the filter still remains better than dynamic programming for k ≤ md-1/(d(logσ m - logσ d))(d-1)/d. These are the first search algorithms for the problem. As side-effects we extend to d dimensions an already proposed algorithm for two-dimensional exact string matching, and we obtain a sublinear-time filter to search in d dimensions allowing k mismatches.