Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
A theory of parameterized pattern matching: algorithms and applications
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Alphabet dependence in parameterized matching
Information Processing Letters
Verifying candidate matches in sparse and wildcard matching
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Data streams: algorithms and applications
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Faster algorithms for string matching with k mismatches
Journal of Algorithms - Special issue: SODA 2000
Parameterized matching with mismatches
Journal of Discrete Algorithms
Approximate parameterized matching
ACM Transactions on Algorithms (TALG)
Efficient string matching in the presence of errors
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Function matching: algorithms, applications, and a lower bound
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Self-normalised distance with don't cares
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Approximate function matching under δ- and γ- distances
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
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We consider the combination of function and permuted matching, each of which has fast solutions in their own right. Given a pattern p of length m and a text t of length n, a function match at position i of the text is a mapping f from @S"p to @S"t with the property that f(p"j)=t"i"+"j"-"1 for all j. We show that the problem of determining for each substring of the text, if any permutation of the pattern has a function match is in general NP-Complete. However where the mapping is also injective, so-called parameterised matching, the problem can be solved efficiently in O(nlog|@S"p|) time. We then give a 1/2-approximation for a Hamming distance based optimisation variant by reduction to multiple knapsack with colour constraints.