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Unformatted text preview: Introduction to Algorithms November 27, 2002 Massachusetts Institute of Technology 6.046J/18.410J Professors Erik Demaine and Shafi Goldwasser Handout 25 Problem Set This is a make-up problem set, only for students who are missing several problems. It is due to your TA on Monday, December 2. Mark the top of each sheet with your name, the course number, the problem number, your recitation section, the date, and the names of any students with whom you collaborated. Each problem should be done on a separate sheet (or sheets) of three-hole punched paper. You will often be called upon to “give an algorithm” to solve a certain problem. Your write-up should take the form of a short essay. A topic paragraph should summarize the problem you are solving and what your results are. The body of your essay should provide the following: 1. A description of the algorithm in English and, if helpful, pseudocode. 2. At least one worked example or diagram to show more precisely how your algorithm works. 3. A proof (or indication) of the correctness of the algorithm. 4. An analysis of the running time of the algorithm. Remember, your goal is to communicate. Graders will be instructed to take off points for convo- luted and obtuse descriptions. Problem-1. Suppose you are given a set of tasks, where task requires units of pro- cessing time to complete, once it has started. You have one computer on which to run these tasks, and the computer can run only one task at a time. A schedule assigns which tasks to run during what times on the computer. For any schedule, let denote the completion time of task , that is, the time at which task completes processing. Your goal is to find a schedule that minimizes the average completion time, that is, one that minimizes (a) Suppose there are two tasks with and . Consider (1) the schedule in which task 1 runs first, followed by task 2 and (2) the schedule in which task 2 runs...
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This note was uploaded on 11/26/2009 for the course CIS 502 taught by Professor Naver during the Spring '09 term at National Tsing Hua University, China.
- Spring '09