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)
The String-to-String Correction Problem
Journal of the ACM (JACM)
A fast algorithm for computing longest common subsequences
Communications of the ACM
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
CPM '97 Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Speeding up transposition-invariant string matching
Information Processing Letters
Fast algorithms for finding disjoint subsequences with extremal densities
Pattern Recognition
On minimizing pattern splitting in multi-track string matching
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
Fast algorithms for finding disjoint subsequences with extremal densities
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Restricted transposition invariant approximate string matching under edit distance
SPIRE'05 Proceedings of the 12th international conference on String Processing and Information Retrieval
A survey of query-by-humming similarity methods
Proceedings of the 5th International Conference on PErvasive Technologies Related to Assistive Environments
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Given strings A and B over an alphabet 驴 驴 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驴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, that are different versions of the edit distance. For all these problems we give algorithms whose time complexities are close to the known upper bounds without transposition invariance. In particular, we show how sparse dynamic programming can be used to solve transposition invariant problems.