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Interval Scheduling Problem - Greedy Algorithm

Learn about the Interval Scheduling Problem and how to solve it using a Greedy Algorithm. Analyze the correctness and runtime of the algorithm.

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Interval Scheduling Problem - Greedy Algorithm

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  1. Lecture 19 CSE 331 Oct 10, 2016

  2. Quiz starts at 1pm and ends at 1:10pm

  3. In 1(b), IGNORE time taken to initialize data structures

  4. Lecture starts at 1:15pm

  5. Pitch grading half done Please wait for grading rubric before asking grading questions

  6. Interval Scheduling Problem Input: n intervals [s(i), f(i)) for 1≤ i ≤ n Output: A scheduleS of the n intervals No two intervals in S conflict |S| is maximized

  7. Analyzing the algorithm R: set of requests S* has no conflicts Set S to be the empty set While R is not empty Choose i in R with the earliest finish time S* is an optimal solution Add i to S Remove all requests that conflict with i from R Return S* = S

  8. Greedy “stays ahead” Greedy OPT

  9. Today’s agenda Prove the correctness Analyze run-time of the greedy algorithm

  10. Algorithm implementation Go through the intervals in order of their finish time 3 How can you tell in O(1) time if any of 2,3 or 4 conflict with 1? Check if s[i] < f(1) 2 1 4 O(n log n) run time In general, if jth interval is the last one chosen Pick smallest i>j such that s[i] ≥ f(j)

  11. The final algo O(n log n) time sort intervals such that f(i) ≤ f(i+1) O(n) time build array s[1..n]s.t. s[i] = start time for i Add 1 to A and set f = f(1) For i = 2 .. n If s[i] ≥ f Add i to A Set f = f(i) Return A* = A

  12. Reading Assignment Sec 4.1of [KT]

  13. Questions?

  14. The “real” end of Semester blues There are deadlines and durations of tasks Write up a term paper Party! Exam study 331 HW Project Monday Tuesday Wednesday Thursday Friday

  15. The “real” end of Semester blues There are deadlines and durations of tasks Write up a term paper Exam study Party! 331 HW Project Monday Tuesday Wednesday Thursday Friday

  16. The algorithmic task YOU decide when to start each task Write up a term paper Exam study You have to do ALL the tasks Party! 331 HW Project Monday Tuesday Wednesday Thursday Friday

  17. Scheduling to minimize lateness All the tasks have to be scheduled GOAL: minimize maximum lateness Write up a term paper Exam study Party! 331 HW Project Monday Tuesday Wednesday Thursday Friday

  18. One possible schedule All the tasks have to be scheduled GOAL: minimize maximum lateness Lateness = 0 Lateness = 2 Exam study Party! 331 HW Write up a term paper Monday Tuesday Wednesday Thursday Friday

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