 Finally, we show that if the input strings do not have long highly periodic substrings, then the gap edit distance problem can be solved in sublinear time within any factor \alpha>1.\tilde{O}{\epsilon^2 k}+k^2\ell).
<meaning-changed>  Finally, we show that if the input strings do not have long highly periodic substrings, then the gap edit distance problem can be solved in sublinear time within any factor \alpha>1.\tilde{O}{\epsilon^2 k}+k^2\ell).
 Finally, we show that if the input strings do not have long highly periodic substrings, then already the k vs (1+\epsilon)k gap edit distance problem can be solved in sublinear time within any factor \alpha>1.\tilde{O}{\epsilon^2 k}+k^2\ell).