Semester Project: Greedy Algorithms and Genome Rearrangements August/17/2012 Name: Xuanyu Hu Professor: Elise de Doncker

Outline 1. Goals of Semester Project 2. Genome Rearrangement 3. Greedy Algorithms 4. Features of Greedy Algorithms 5. Sorting by Reversals Problem 6. Greedy Algorithms in Genome Rearrangement 7. Project Testing

Goals 1. Know the result of Genome Rearrangement 2. Know what are Greedy Algorithms 3. Use Greedy Algorithms to solve Genome Rearrangement problem

Genome Rearrangements Every genome rearrangement results in a change of gene ordering, and a series of these rearrangements can alter the genomic architecture of a species.

Greedy Algorithms A greedy algorithm is an algorithm that follows the problem solving heuristic of making the locally optimal choice at each stage with the hope of finding a global optimum.

Features of Greedy Algorithms In many problems, a greedy strategy does not in general produce an optimal solution, but nonetheless a greedy heuristic may yield locally optimal solutions that approximate a global optimal solution in a reasonable time.

Sorting by Reversals Problem SIMPLEREVERSALSORT(π) 1 for i ← 1 to n-1 2 j ← position of element i in π 3 if j ≠ i 4 π ← π * ρ (i, j) 5 output π 6 if π is the identity permutation 7 return

Project Testing 1

Problem Reversal Distance Problem: Given two permutations π and π', find a series of reversals that transforms π into π'.

Input and output Input: Permutation π and π' Output: All of the permutations that it goes through in order to transform π into π' with one line after each reversal and the number of reversals.

Project Testing 2

Project Testing 3

Conclusion and Questions 1. Goals of Semester Project 2. Definition of Genome Rearrangement 3. Greedy Algorithms 4. Features of Greedy Algorithms 5. Sorting by Reversals Problem 6. Greedy Algorithms in Genome Rearrangement 7. Project Testing

References Greedy/greedyIntro.htm 5. eleven/ al.pgen