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On-line Approximate String Matching with Bounded Errors

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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 *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 differences
for
edit distance, and *s* the alphabet size. Our experimental results show
the practicality of this novel and promising research direction.
Finally, we extend the proposed approach to the multiple approximate
string matching setting, where the approximate occurrence of *r*
patterns are simultaneously sought.
Again, we can break the average-case optimal lower bound of the classical
problem, achieving average case
*O(n log_s(rm)/m)* time with any *e = poly(k/m)*.