Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Scaling algorithms for network problems
Journal of Computer and System Sciences
Improved string matching with k mismatches
ACM SIGACT News
Efficient string matching with k mismatches
Theoretical Computer Science
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Fast string matching with k-differences
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
Faster scaling algorithms for network problems
SIAM Journal on Computing
International Journal of Computer Vision
A theory of parameterized pattern matching: algorithms and applications
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
An Alphabet Independent Approach to Two-Dimensional Pattern Matching
SIAM Journal on Computing
Alphabet dependence in parameterized matching
Information Processing Letters
Parameterized pattern matching: algorithms and applications
Journal of Computer and System Sciences
Parameterized Duplication in Strings: Algorithms and an Application to Software Maintenance
SIAM Journal on Computing
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Faster suffix tree construction with missing suffix links
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A fast string searching algorithm
Communications of the ACM
Separable attributes: a technique for solving the sub matrices character count problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A Decomposition Theorem for Maximum Weight Bipartite Matchings
SIAM Journal on Computing
Faster algorithms for the construction of parameterized suffix trees
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Parameterized matching with mismatches
Journal of Discrete Algorithms
Function matching: algorithms, applications, and a lower bound
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
On the Longest Common Parameterized Subsequence
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
δ γ --- Parameterized Matching
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
Counting Parameterized Border Arrays for a Binary Alphabet
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
On the longest common parameterized subsequence
Theoretical Computer Science
Information Processing Letters
Verifying a parameterized border array in O(n1.5) time
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Parameterized searching with mismatches for run-length encoded strings
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Verifying and enumerating parameterized border arrays
Theoretical Computer Science
The set of parameterized k-covers problem
Theoretical Computer Science
Parameterized searching with mismatches for run-length encoded strings
Theoretical Computer Science
Approximate function matching under δ- and γ- distances
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
Information Sciences: an International Journal
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Two equal length strings s and s′, over alphabets Σs and Σs′, parameterize match if there exists a bijection π : Σs → Σs′ such that π (s) = s′, where π (s) is the renaming of each character of s via π. Parameterized matching is the problem of finding all parameterized matches of a pattern string p in a text t, and approximate parameterized matching is the problem of finding at each location a bijection π that maximizes the number of characters that are mapped from p to the appropriate |p|-length substring of t. Parameterized matching was introduced as a model for software duplication detection in software maintenance systems and also has applications in image processing and computational biology. For example, approximate parameterized matching models image searching with variable color maps in the presence of errors. We consider the problem for which an error threshold, k, is given, and the goal is to find all locations in t for which there exists a bijection π which maps p into the appropriate |p|-length substring of t with at most k mismatched mapped elements. Our main result is an algorithm for this problem with O(nk1.5 + mk log m) time complexity, where m = |p| and n=|t|. We also show that when |p| = |t| = m, the problem is equivalent to the maximum matching problem on graphs, yielding a O(m + k1.5) solution.