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Figure 2 | Algorithms for Molecular Biology

Figure 2

From: Lossless filter for multiple repeats with bounded edit distance

Figure 2

Detection of ( L , d , r )-repeats and two overlapping parallelograms. Two parallelograms that overlap. The dark grey parallelogram in the figure detects q-hits between w = s[a, a + L - 1] and any word w k = s[i, j] with i [c + a, c + d + a] and j [c + a + L - 1, c + d + a + L - 1]. The word z = s[c + a, c + d + a + L - 1] of length L + d contains the word w k which in turn contains the word x = s[c + d + a, c + a + L - 1] of length L - d. Analogously for the light gray parallelogram, the word z' = s[c' + a, c' + d + a + L - 1] of length L + d contains a word w k MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGafm4DaCNbauaadaWgaaWcbaGaem4AaSgabeaaaaa@2EE3@ which in turn contains the word x' = s[c' + d + a, c' + a + L - 1] of length L - d. The words w k and w k MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGafm4DaCNbauaadaWgaaWcbaGaem4AaSgabeaaaaa@2EE3@ are not shown because their length is variable. They necessarily overlap because they both contain the word p = s[c' + d + a, c + a + L - 1], that is the overlap between x and x'.

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