Algorithms for approximate string matching
Information and Control
SIAM Journal on Computing
Dynamic programming with convexity, concavity and sparsity
Theoretical Computer Science - Selected papers of the Combinatorial Pattern Matching School
Sparse dynamic programming I: linear cost functions
Journal of the ACM (JACM)
Text algorithms
Tree pattern matching and subset matching in randomized O(nlog3m) time
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Tree pattern matching and subset matching in deterministic O(n log3 n)-time
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
The String-to-String Correction Problem
Journal of the ACM (JACM)
A fast algorithm for computing longest common subsequences
Communications of the ACM
Verifying candidate matches in sparse and wildcard matching
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A sub-quadratic sequence alignment algorithm for unrestricted cost matrices
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate string matching with gaps
Nordic Journal of Computing
Three Heuristics for delta-Matching: delta-BM Algorithms
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
CPM '97 Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching
Time-series similarity problems and well-separated geometric sets
Nordic Journal of Computing
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
On minimizing pattern splitting in multi-track string matching
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
Sequential and indexed two-dimensional combinatorial template matching allowing rotations
Theoretical Computer Science
Speeding up transposition-invariant string matching
Information Processing Letters
Rotation and lighting invariant template matching
Information and Computation
Algorithms for computing variants of the longest common subsequence problem
Theoretical Computer Science
A Simple Algorithm for Transposition-Invariant Amplified (δ, γ)-Matching
IEICE - Transactions on Information and Systems
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Given strings A = a1a2...am and B = b1b2...bn over an alphabet Σ ⊆ U, where U is some numerical universe closed under addition and subtraction, and a distance function d(A, B) that gives the score of the best (partial) matching of A and B, the transposition invariant distance is mint∈U{d(A + t, B)}, where A + t = (a1 + t)(a2 + t)...(am + t). We study the problem of computing the transposition invariant distance for various distance (and similarity) functions d, including Hamming distance, longest common sabsequence (LCS), Levenshtein distance, and their versions where the exact matching condition is replaced by an approximate one. For all these problems we give algorithms whose time complexities are close to the known upper bounds without transposition invariance, and for some we achieve these upper bounds. In particular, we show how sparse dynamic programming can be used to solve transposition invariant problems, and its connection with multidimensional range-minimum search. As a byproduct, we give improved sparse dynamic programming algorithms to compute LCS and Levenshtein distance.