### On-line Approximate String Matching with Bounded Errors

#### Marcos Kiwi, Gonzalo Navarro, and Claudio Telha

We introduce a new dimension to the widely studied on-line approximate string matching problem, by introducing an {\em error threshold} parameter e so that the algorithm is allowed to miss occurrences with probability e. This is particularly appropriate for this problem, as approximate searching is used to model many cases where exact answers are not mandatory. We show that the relaxed version of the problem allows us breaking the average-case optimal lower bound of the classical problem, achieving average case O(n log_s(m)/m) time with any e = poly(k/m), where n is the text size, m the pattern length, k the number of errors for edit distance, and s the alphabet size. Our experimental results show the practicality of this novel and promising research direction.