hw6(4) - CS 373U Homework 6 (Practice only) Spring 2004 1....

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CS 373U Homework 6 (Practice only) Spring 2004 1. Let P be a set of n points in the plane. Recall that a point p P is Pareto-optimal if no other point is both above and to the right of p . Intuitively, the sorted sequence of Pareto-optimal points describes a staircase with all the points in P below and to the left. Your task is to describe some algorithms that compute this staircase. The staircase of a set of points (a) Describe an algorithm to compute the staircase of P in O ( nh ) time, where h is the number of Pareto-optimal points. (b) Describe a divide-and-conquer algorithm to compute the staircase of P in O ( n log n ) time. [Hint: I know of at least two diFerent ways to do this.] (c) Describe an algorithm to compute the staircase of P in O ( n log h ) time, where h is the number of Pareto-optimal points. [Hint: I know of at least two diFerent ways to do this.] (d) Finally, suppose the points in P are already given in sorted order from left to right. Describe an algorithm to compute the staircase of P in O ( n ) time. [Hint: I know of at least two diFerent ways to do this.] 2. Let R be a set of n rectangles in the plane. (a) Describe and analyze a plane sweep algorithm to decide, in
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hw6(4) - CS 373U Homework 6 (Practice only) Spring 2004 1....

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