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Fig. 1 | Algorithms for Molecular Biology

Fig. 1

From: Super short operations on both gene order and intergenic sizes

Fig. 1

A sequence of two super short reversals and one super short transposition that transforms \(\pi = (1~3~4~2~5)\), with \(r^\pi = (3,5,2,1,2,8)\) into \(\iota = (1,2,3,4,5)\), with \(r^\iota = (3,2,6,4,5,1)\). Intergenic regions are represented by rectangles, whose dimensions vary according to their sizes. The 1-reversal \(\rho (5,5,2,7)\) applied in a transforms \(\pi\) into \(\pi ' = \pi\), and it cuts \(\pi\) after position 2 at \(r^\pi _5\) and after position 7 at \(r^\pi _6\), resulting in \(\ell (r^{\pi '}_5) = 9\), \(\ell (r^{\pi '}_6) = 1\), and \(r^{\pi '} = (3,5,2,1,9,1)\). The 2-reversal \(\rho (3,4,1,5)\) applied in b transforms \(\pi '\) into \(\pi '' = (1~3~2~4~5)\), and it cuts \(\pi '\) after position 1 at \(r^{\pi '}_3\) and after position 5 at \(r^{\pi '}_5\), resulting in \(\ell (r^{\pi ''}_3) = 6\), \(\ell (r^{\pi ''}_5) = 5\), and \(r^{\pi ''} = (3,5,6,1,5,1)\). Finally, the 2-transposition \(\tau (2,3,4,0,4,1)\) applied in c transforms \(\pi ''\) into \(\iota\), and it cuts \(\pi ''\) in position 0 at \(r^{\pi ''}_2\), after position 4 at \(r^{\pi ''}_3\), and after position 1 at \(r^{\pi ''}_4\), resulting in \(\ell (r^{\pi ''}_3) = 6\), \(\ell (r^{\pi ''}_5) = 5\), and \(r^{\pi ''} = (3,5,6,1,5,1)\). as shown in d

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