# Permuted Function Matching

Rapha?, Benjamin Sach, Permuted Function Matching. *Information Processing Letters*, 110(22), pp. 1012–1015. October 2010. PDF, 130 Kbytes.
## Abstract

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 Sigma_p to Sigma_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(n log |Sigma_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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