1. Chap. 7 Genome Rearrangements Introduction to Computational Molecular Biology Chap. 7.2.5 ~ 7.3.2

2. Bad Components Hurdle do not separate any other two bad components Non-hurdle separate any pair of bad component Super hurdle if its removal would cause some non-hurdle to become hurdle Simple hurdles All other hurdles Bad Components NonhurdlesHurdles Simple HurdlesSuper Hurdles  “Bad component” consists entirely of bad cycles  Bad component hierarchy

3. Bad Components Fortress A permutation which contains odd number of hurdles and all of them are super hurdles Lower Bound on the Reversal Distance Non-Hurdle

4. Special kind of reversal Hurdle cutting Reversal on convergent edges Not change c(  ) and decreases h(  ) When h(  ) is odd, the hurdle is simple Hurdle merging Reversal on edges of different cycles Decrease c(  ) and decrease h(  ) by two When h(  ) is even, merging opposite hurdles Two hurdles become good components, as well as any non- hurdle that separates them

5. Algorithm Input: Permutations  and  Output: sorting reversal for  with target  If there is a good component then Pick two divergent edges e, f. and Reverse if result creates not a bad component Return Else if the number of hurdles is even then Merge 2 opposite hurdles Return Else If there is a simple hurdle then cut it. Return Else merge two hurdles. Return

6. Unoriented Blocks Unoriented permutation  Mapping from {1,2,…,n} to a set L of n labels In this book, Identity permutation is target Reversal Same as oriented permutation but except flipping arrow

7. Strips Strip A sequence of consecutive labels surrounded by breakpoints but with no internal breakpoints Increasing or Decreasing strip A single label is an increasing and decreasing strip ‘L’, ‘R’ are always part of a single increasing strip L 1 2 8 7 3 5 6 4 R Increasing Strip Decreasing Strip Increasing and Decreasing Strip

8. Theorem 7.4 If Label k belongs to a decreasing strip k-1 belongs to an increasing strip then there is a reversal that removes at least one breakpoint Theorem 7.5 If Label k belongs to a decreasing strip K+1 belongs to an increasing strip then there is a reversal that removes at least one breakpoint … (k-1) … k … … k … (k-1) … … (k+1) … k … … k … (k+1) … Theorem

9. Theorem 7.6 Let  be a permutation with a decreasing strip If No breakpoint-removing reversal leaves a decreasing strip then there is a reversal that removes two breakpoint from  Theorem 7.7 The number of iterations in algorithm Sorting Unoriented Permutation is less than or equal to the number of breakpoints in the initial permutation … (k-1) … k … … l … (l+1) … Theorem

10. Algorithm Input: Permutations  Output: sorting reversal for  with target  If there is a good component then Pick two divergent edges e, f. and Reverse if result creates not a bad component Return Else if the number of hurdles is even then Merge 2 opposite hurdles Return Else If there is a simple hurdle then cut it. Return Else merge two hurdles. Return