HW4 Handout - CSc 445: Homework Assignment 4 Assigned:...

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Unformatted text preview: CSc 445: Homework Assignment 4 Assigned: Wednesday March 12 2008, Due: 10:30 AM, Monday March 31 2008 Clear, neat and concise solutions are required in order to receive full credit. Revise your work carefully before submission, and consider how your work is presented. If you cannot solve a particular problem, state this clearly in your write-up, and write down only what you know to be correct. For involved proofs, first outline the argument and then delve into the details. 1. (10 pts) A company that needs to buy n different pieces of software. Because of bureaucratic regula- tions, the company can only buy one per month. Currently all needed software is priced at $100 but the cost for software i increases by a factor of c i > 1 each month for all i . Assuming c i negationslash = c j for any i negationslash = j , in what order should the company buy the needed software so as to minimize costs? Design and analyze an algorithm that takes n growth rates c 1 ,c 2 ,...,c n and computes an order that minimizes costs. 2. (10 pts) Recall the set cover problem and the greedy algorithm discussed in class. Argue why greedy ensures that n t +1 n t n t /k where n t is the number of towns not covered after t iterations of the greedy algorithm and k is the size of the optimal solution. 3. (10 pts) Recall the Appalachian trail problem but now we would like to schedule some maintenance work on the shelters along it. In particular, each maintenance crew will be responsible for a 10mile chunk of the trail. Design and analyze an algorithm for minimizing the number of crews needed,chunk of the trail....
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HW4 Handout - CSc 445: Homework Assignment 4 Assigned:...

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