Average-optimal single and multiple approximate string matching

We present a new algorithm for multiple approximate string matching. It is based on reading backwards enough `-grams from text windows so as to prove that no occurrence can contain the part of the window read, and then shifting the window. We show analytically that our algorithm is optimal on average. Hence our first contribution is to fill an important gap in the area, since no average-optimal algorithm existed for multiple approximate string matching. We consider several variants and practical improvements to our algorithm, and show experimentally that they are resistant to the number of patterns and the fastest for low difference ratios, displacing the long-standing best algorithms. Hence our second contribution is to give a practical algorithm for this problem, by far better than any existing alternative in many cases of interest. On real life texts, our algorithm is especially interesting for computational biology applications. In particular, we show that our algorithm can be successfully used to search for one pattern, where many more competing algorithms exist. Our algorithm is also average-optimal in this case, being the second after that of Chang and Marr. However, our algorithm permits higher difference ratios than Chang and Marr, and this is our third contribution