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hw4 - CSCI 4041 Algorithms and Data Structures(Fall09...

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CSCI 4041: Algorithms and Data Structures (Fall’09) Homework 4, Due 11/24/09 Answer all of the following questions, and always explain your answer. Good Luck! 1. (50 points) Consider the activity selection problem with a set S = { a 1 , . . . , a n } of n proposed activi- ties that wish to use a resource, e.g., different courses planning to use a classroom. Each activity has a known start time s i and a finish time f i where s i f i . Activities a i and a j are compatible if the intervals [ s i , f i ) and [ s j , f j ) do not overlap. The activity selection problem is to find a maximum-size set of mutually compatible events. (a) (25 points) Assuming the activities have been sorted based on the finish times, give a bottom-up dynamic-programming algorithm for solving the activity-selection problem using the recurrence on c [ i, j ] , the number of activities in a maximum-size subset of mutually compatible activities in S i,j . What is the complexity of the dynamic programming algorithm?
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