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Put yourself in the shoes of the famous Tommy Wiseau. Imagine you want to make a movie. But a tornado has torn through your film room, and you are close to a deadline. You had already put together n clips into a single film, but now clips are strewn everywhere on the floor. More specifically, you had m bundles of clips, each containing a single copy of each of the n clips. Now, some bundles are missing some clips. You know which clips are still in each bundle, and you need to quickly grab k of the bundles to try to reassemble as much of the ful movie as possible. The problem k-BUNDLE MOVIE consists of taking k m incomplete bundles and using the clips in them to try to reconstruct as much of the original movie as possible. That is, select k bundles that maximize the number of clips collectively contained in them. Describe a straightforward greedy approximation algorithm for k-BUNDLE MOVIE, and show that its approximation factor is21-1/e. (Hint: Use the Pigeonhole Principle, and the fact that (1-1/-1/e for all k E N.) Put yourself in the shoes of the famous Tommy Wiseau. Imagine you want to make a movie. But a tornado has torn through your film room, and you are close to a deadline. You had already put together n clips into a single film, but now clips are strewn everywhere on the floor. More specifically, you had m bundles of clips, each containing a single copy of each of the n clips. Now, some bundles are missing some clips. You know which clips are still in each bundle, and you need to quickly grab k of the bundles to try to reassemble as much of the ful movie as possible. The problem k-BUNDLE MOVIE consists of taking k m incomplete bundles and using the clips in them to try to reconstruct as much of the original movie as possible. That is, select k bundles that maximize the number of clips collectively contained in them. Describe a straightforward greedy approximation algorithm for k-BUNDLE MOVIE, and show that its approximation factor is21-1/e. (Hint: Use the Pigeonhole Principle, and the fact that (1-1/-1/e for all k E N.)

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