Pattern Matching with Pair Correlation Distance

In pattern matching with pair correlation distance problem, the goal is to find all occurrences of a pattern P of length m, in a text T of length n, where the distance between them is less than a threshold k. For each text location i, the distance is defined as the number of different kinds of mismatched pairs (α,β), between P and T[i ...i + m]. We present an algorithm with running time of O(min{|ΣP|2nlogm,n(mlogm)23})O(min{|ΣP|2nlog⁡m,n(mlog⁡m)23}) for this problem. Another interesting problem is the one-side pair correlation distance where it is desired to find all occurrences of P where the number of mismatched characters in P is less than k. For this problem, we present an algorithm with running time of O(min{|ΣP|nlogm,nmlogm−−−−−−−√})O(min{|ΣP|nlog⁡m,nmlog⁡m}).