lecture_08a

# lecture_08a - Interval Scheduling Interval scheduling Job j...

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Interval Scheduling Interval scheduling. s Job j starts at s j and finishes at f j . s Two jobs are compatible if they don't overlap. s Goal : find the largest subset of mutually compatible jobs. 1 TIME

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Interval Scheduling: Greedy Algorithms Greedy template . s Sort the jobs in some order, start time. s Consider the job one by one; accept a job if it's compatible with the ones already accepted . 2
Example: earliest finish time A C B D E Time 0 F G 1 2 3 4 5 6 7 8 9 10 11 H 0 1 2 3 4 5 6 7 8 9 10 11

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A C B D E 0 1 2 3 4 5 6 7 8 9 10 11 B Time 0 F G 1 2 3 4 5 6 7 8 9 10 11 H
A C B D E 0 1 2 3 4 5 6 7 8 9 10 11 B C Time 0 F G 1 2 3 4 5 6 7 8 9 10 11 H

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A C B D E 0 1 2 3 4 5 6 7 8 9 10 11 B A Time 0 F G 1 2 3 4 5 6 7 8 9 10 11 H
A C B D E 0 1 2 3 4 5 6 7 8 9 10 11 B E Time 0 F G 1 2 3 4 5 6 7 8 9 10 11 H

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A C B D E 0 1 2 3 4 5 6 7 8 9 10 11 B E D Time 0 F G 1 2 3 4 5 6 7 8 9 10 11 H
A C B D E 0 1 2 3 4 5 6 7 8 9 10 11 B E F Time 0 F G 1 2 3 4 5 6 7 8 9 10 11 H

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A C B D E 0 1 2 3 4 5 6 7 8 9 10 11 B E G Time 0 F G 1 2 3 4 5 6 7 8 9 10 11 H
A C B D E 0 1 2 3 4 5 6 7 8 9 10 11 B E H Time 0 F G 1 2 3 4 5 6 7 8 9 10 11 H

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Interval Scheduling: Greedy Algorithms Greedy template . Sort the jobs in some order. Consider the job one by one; accept a job if it's compatible with the ones already accepted . s [Earliest start time] Consider jobs in ascending order f start time s 12 of start time s j . s [Earliest finish time] Consider jobs in ascending order of finish time f j . s
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lecture_08a - Interval Scheduling Interval scheduling Job j...

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