Given a rational number n, n >= 0, with denominator strictly positive, decompose this number as a sum of rationals with numerators equal to one and without repetitions.

A filter is presented that reduces big ‘common substring problems' to a more manageable size. The approach uses ‘shingling’ and ‘fingerprinting’: In a first step the fingerprints of the reference string are scattered over a large hash map. Gathered in a second step, these hash values are matched against the values obtained from the test string.