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Table 2 Traces of sequences sorting R. felis into its ancestor

From: An asymmetric approach to preserve common intervals while sorting by reversals

Trace Trace normal form (f) # seq. # seq.
  Subtrace representative (e) trace subtr.
1. f = {2, 3}{3}{4,..., 11}{5}{5, 8, 9, 10}{7}{8, 10} < {5, 6, 7}{8, 9} 90720 45360
  e = {4,..., 11}{5, 8, 9, 10}{8, 10}{8, 9}{5, 6, 7}{2, 3}{3}{7}{5}   
2. f = {2, 3}{3}{4,..., 11}{5,..., 10}{6}{6, 7, 8, 10}{6, 8} < {6,..., 9}{7, 8} 90720 45360
  e = {2, 3}{3}{4,..., 11}{5,..., 10}{6}{6, 7, 8, 10}{6, 8}{6,..., 9}{7, 8}   
3. f = {2, 3}{3}{4,..., 11}{5,..., 10}{6}{6, 8, 9, 10}{8, 10} < {7,..., 10}{8, 9} 90720 45360
  e = {2, 3}{3}{4,..., 11}{5,..., 10}{6}{6, 8, 9, 10}{7,..., 10}{8, 10}{8, 9}   
4. f = {2, 3}{3}{4,..., 11}{5,..., 10}{6, 7, 8, 10}{7}{9} < {6, 7, 9} < {8, 9} 60480 60480
  e = {2, 3}{3}{4,..., 11}{5,..., 10}{6, 7, 8, 10}{7}{9}{6, 7, 9}{8, 9}   
5. f = {2, 3}{3}{4,..., 11}{5,..., 10}{6, 8}{9}{10} < {6, 9, 10} < {7,..., 10} 60480 0
6. f = {2, 3}{3}{4,..., 11}{5,..., 10}{7}{8, 10}{10} < {6, 7, 10} < {6,..., 9} 60480 0
7. f = {2, 3}{3}{4,..., 11}{5, 9, 10}{7}{9}{10} < {5, 8} < {5, 6, 7} 60480 60480
  e = {2, 3}{3}{4,..., 11}{5, 9, 10}{7}{9}{10}{5, 8}{5, 6, 7}   
8. f = {2, 3}{3}{4,..., 11}{5, 8, 9, 10}{5, 9, 10}{7} < {5, 6, 7, 9, 10} < {6, 7, 8, 10} < {6,..., 9} 9072 0
9. f = {2, 3}{3}{4,..., 11}{5, 8, 9, 10}{6}{8, 10} < {5, 6, 8, 9} < {5, 7, 8, 9} < {6,..., 9} 6048 0
10. f = {2, 3}{3}{4,..., 11}{5, 9, 10}{6, 8}{10} < {5, 6, 9} < {5, 7, 8, 9} < {6,..., 9} 6048 0
11. f = {2, 3}{3}{4,..., 11}{6}{6, 8, 9, 10} < {5, 6, 8, 10} < {5, 6, 8, 9} < {5,..., 8}{7, 8} 6048 6048
  e = {2, 3}{3}{4,..., 11}{6}{6, 8, 9, 10}{5, 6, 8, 10}{5, 6, 8, 9}{5,..., 8}{7, 8}   
12. f = {2, 3}{3}{4,..., 11}{5}{6, 8, 9, 10} < {5, 6, 8, 10} < {5, 7, 9} < {6, 7, 9} < {8, 9} 3024 0
13. f = {2, 3}{3}{4,..., 11}{6, 8} < {6, 9, 10}{7, 8} < {5, 6, 10} < {5, 6, 9} < {5,..., 8} 2520 0
  Total 546840 263088
  1. The 546840 sequences that sort Rfe = (1, 3, -2, -11, 5, -9, -10, 8, 6, -7, -4, 12) (R. felis) into R 2 = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) are distributed in 13 traces. Each trace is represented by its normal form. The third column indicates the number of sequences in each trace. When we apply the progressive detection of common intervals, accepting at most two common interval breaks, we obtain 263088 sequences distributed in 6 progressive near-perfect subtraces (subsets of traces 1, 2, 3, 4, 7 and 11). Each progressive near-perfect subtrace is represented by a 2-tuple (e is the subtrace representative, f is the trace normal form). The fourth column gives the number of sequences in each subtrace.