Order-Preserving Pattern Matching with k Mismatches

We study a generalization of the order-preserving pattern matching recently introduced by Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.), where 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 variant, 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 + k log log k)) time.