| Popis: |
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. |
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