Semester Project:Semester Project:Greedy Algorithms and GeGreedy Algorithms and Ge

nome Rearrangementsnome Rearrangements

August/17/2012August/17/2012Name: Xuanyu HuName: Xuanyu Hu

Professor: Elise de DonckerProfessor: 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 Rearran

gement• 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 Rearran

gement• 7. Project Testing

References1.http://bix.ucsd.edu/bioalgorithms/downloads/code/ 2.http://en.wikipedia.org/wiki/Greedy_algorithm3.http://en.wikipedia.org/wiki/Greedy_algorithm4.http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/

Greedy/greedyIntro.htm 5.http://www.catonmat.net/blog/mit-introduction-to-algorithms-part-elev

en/ 6.http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=11899 7.http://dimacs.rutgers.edu/BMC/TeacherMaterials/Rearrange.pdf 8.http://genome.cshlp.org/content/13/1/37.full 9.http://www.plosgenetics.org/article/info%3Adoi%2F10.1371%2Fjourn

al.pgen.1000128 10.http://lib.bioinfo.pl/courses/view/693 11.http://lib.bioinfo.pl/courses/view/693 12.http://en.wikipedia.org/wiki/Bioinformatics