# hw5(10) - CS 573 Homework 5 (due November 19, 2010) Fall...

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CS 573 Homework 5 (due November 19, 2010) Fall 2010 CS 573: Graduate Algorithms, Fall 2010 Homework 5 Due Friday, November 19, 2010 at 5pm (in the homework drop boxes in the basement of Siebel) 1. Suppose we are given a set of boxes, each speciﬁed by their height, width, and depth in centimeters. All three side lengths of every box lie strictly between 10cm and 20cm. As you should expect, one box can be placed inside another if the smaller box can be rotated so that its height, width, and depth are respectively smaller than the height, width, and depth of the larger box. Boxes can be nested recursively. Call a box is visible if it is not inside another box. Describe and analyze an algorithm to nest the boxes so that the number of visible boxes is as small as possible. 2. Suppose we are given an array A [ 1.. m ][ 1.. n ] of non-negative real numbers. We want to round A to an integer matrix, by replacing each entry x in A with either b x c or d x e , without changing the sum of entries in any row or column of A . For example: 1.2 3.4 2.4 3.9 4.0 2.1 7.9 1.6 0.5 7-→ 1 4 2 4 4 2 8 1 1 Describe an efﬁcient algorithm that either rounds A in this fashion, or reports correctly that no such rounding is possible. 3. The Autocratic Party is gearing up their fund-raising campaign for the 2012 election. Party

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## This note was uploaded on 01/22/2012 for the course CS 573 taught by Professor Chekuri,c during the Fall '08 term at University of Illinois, Urbana Champaign.

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hw5(10) - CS 573 Homework 5 (due November 19, 2010) Fall...

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