# lect12 - Lecture 12 Greedy Strategy Exchange Property For...

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Lecture 12 Greedy Strategy

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Exchange Property For some problems without matroid structure, the greedy strategy may also work for obtaining optimal sultions. An significant observation is that those successful cases usually connecting to certain (simple) exchange property.
Activity Selection Problem

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Mathematical Model . ) , [ ) , [ : ping nonoverlap y. cardinalit the maximize to intervals ping nonoverlap of subset a find ), , [ ),. .., , [ ), , [ intervals of set a Given 2 2 1 1 = j j i i n n f s f s f s f s f s
Exchange Property solution. maximum in the interval 1st with the ) , [ exchange always can we , ) , [ interval ithout solution w maximum a In . Suppose 1 1 1 1 2 1 f s f s f f f n

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Greedy Algorithm . return )}; , {[ then in interval any with overlap not does ) , [ if do to 1 for ; . Sort 2 1 S f s S S S f s n i S f f f i i i i n
}. ) , [ ) , [ | ) , {[ set for solution optimal an is )} , {[ * ) 2 ( . * solution

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lect12 - Lecture 12 Greedy Strategy Exchange Property For...

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