exercise5 - CSE5311 Design and Analysis of Algorithms Fall...

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CSE5311 Design and Analysis of Algorithms Fall 2009 September 28, 2009 Exercise Set 5 1. Suppose you are managing the construction of billboards on the Stephen Daedalus Memorial Highway, a heavily traveled stretch of road that runs west-east for M miles. The possible sites for billboards are given by numbers x 1 ,x 2 ,…,x n , each in the interval [ 0,M ] (specifying their position along the highway measured in miles from its western end). If you place a billboard at location x i , you receive a revenue of r i > 0. Regulations imposed by the county’s Highway Department require that no two billboards be within less than or equal to 5 miles of each other. You’d like to place billboards at a subset of sites so as to maximize your total revenue, subject to this restriction. 2. Design a dynamic programming algorithm for the change-making problem : given an amount n and unlimited quantities of coins of each of the denominations d 1 , d 2 , . .. d m , find the smallest number of coins that add up to n or indicate that the problem does not have a solution. 3. Suppose we want to replicate a file over a collection of n servers, labeled S 1 ,S 2 ,…, S n . To place a copy of the file at server S i results in a placement cost of c i , where c i is an integer greater than 0. Now if a user requests the file from server S i , and no copy of the file is present at S i , then servers S i+1 ,S i+2 ,…, S i+3 … are searched in order until a copy of the file is finally found, say at server S j , where j > i. This results in an access cost of
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exercise5 - CSE5311 Design and Analysis of Algorithms Fall...

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