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2011/1/18 NPC seminar slide

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- 1. Greedy is Good Greedy Algorithm
- 2. Introduction• Greedy algorithm always makes the choice that looks best at the moment, with hoping that a locally optimal choice will lead to a global optimum• Similar to Dynamic Programming, it applies to Optimization Problem• It is usually easy to think up and implement• Most problems for which they work well have two properties – Greedy choice property – Optimal substructure
- 3. Greedy choice property• Greedy algorithm never reconsiders its choices• This is main difference from dynamic programming
- 4. Optimal substructure• Optimal solution to the problem contains optimal solution to the sub-problems
- 5. Activity Selection problem• Activity Selection problem is to select the maximum number of activities that can be performed by a single person or machine within a time frame , given a set of activities each marked by start time and finish time• Formal definition – number of activity: n – start time of activity i is si – finish time of activity i is fi – non-conflicting activities i and j: si≥fj or sj≥fi – Find the maximum set (S) of non-conflicting activities
- 6. Early Finish Greedy• Activity Selection problem has optimal substructure – Assume that activities are sorted by monotonically increasing finish time – Aij = Aik ∪ {ak} ∪ Akj• Select the activity with the earliest finish• Eliminate the activities that are in conflict• Repeat until there is no remains
- 7. Early Finish Greedy
- 8. Early Finish Greedy
- 9. Early Finish Greedy
- 10. Early Finish Greedy
- 11. Early Finish Greedy
- 12. Early Finish GreedySort the set of activities by finishing time (f[i])S=1f = f[1]for i=1 to n if s[i] ≥ f S=SUi f = f[i]end for
- 13. Cases of failure• Greedy algorithms don’t always yields on optimal solution• Ex) How can a given amount of money be made with the least number of coins of given denominations? – Target amount: 6 – Denominations: 1, 3, 4 – Greedy solution: (4, 1, 1) – Optimal solution: (3, 3)
- 14. Conclusion• Greedy algorithms are usually easy to think of, easy to implement and run fast,• but it may fail to produce the optimal solution• Mathematical concepts may give you a recipe for proving that a problem can be solved with greedy, but it ultimately comes down to the experience of the programmer.
- 15. References• http://en.wikipedia.org/wiki/Greedy_algorithm• http://www.topcoder.com/tc?module=Static&d1=tu torials&d2=greedyAlg• http://security.re.kr/~sjkim/LectureNotes/SKKU/201 0/CSE3002/Lec13(Alg).pdf

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