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hbs8(1) - CS 473 HBS 8 Spring 2009 CS 473 Undergraduate...

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CS 473 HBS 8 Spring 2009 CS 473: Undergraduate Algorithms, Spring 2009 HBS 8 1. A box i can be specified by the values of its sides, say ( i 1 , i 2 , i 3 ) . We know all the side lengths are larger than 10 and smaller than 20 (i.e. 10 < i 1 , i 2 , i 3 < 20). Geometrically, you know what it means for one box to nest in another: It is possible if you can rotate the smaller so that it fits inside the larger in each dimension. Of course, nesting is recursive, that is if i nests in j and j nests in k then i nests in k . After doing some nesting operations, we say a box is visible if it is not nested in any other one. Given a set of boxes (each specified by the lengthes of their sides) the goal is to find a set of nesting operations to minimize the number of visible boxes. Design and analyze an efficient algorithm to do this. 2. Let the number of papers submitted to a conference be n and the number of available reviewers be m . Each reviewer has a list of papers that he / she can review and each paper should be reviewed by three different persons. Also, each reviewer can review at most 5 papers. Design and analyze
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