Order-preserving pattern matching with k mismatches

We consider a generalization of the recently introduced order-preserving pattern matching. The difference between the standard pattern matching and the order-preserving variant is that instead of looking for an exact copy of the pattern, we only require that the relative order between the elements is the same. In our generalization, we additionally allow up to k mismatches between the pattern of length m and the text of length n, and the goal is to construct an efficient algorithm for small values of k. Our solution detects an order-preserving occurrence with up to k mismatches in O(n(log log m+klog log k)) time.