sol8 - Introduction to Algorithms CS 482, Spring 2008...

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Introduction to Algorithms Solution Set 8 CS 482, Spring 2008 (1) The algorithm resembles the Greedy-Balance algorithm given in Section 11.1. For each machine M i , we maintain a variable T i which keeps tracks of the total amount of time required for M i to process all of the jobs that have been assigned to it by the algorithm so far. Initially all jobs are unassigned, and T i = 0 for all i . We run through the jobs in arbitrary order. Each job is assigned to the machine M i with the minimum current load, M i = arg min j ( T j ) . The load on M i is then updated to reflect the new job that has been assigned to it; thus we increase T i by either t i or 1 2 t i depending on whether M i is a slow machine or a fast machine. The main loop of the algorithm has n iterations. In a na¨ ıve implementation, each loop iteration requires O ( m + k ) work to find the machine with the minimum current load, and O (1) work to update the load on that machine, for a total running time of O ( n ( m + k )) . Using a heap to store the values T i , one can reduce the running time to
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This note was uploaded on 10/02/2008 for the course CS 482 taught by Professor Kleinberg during the Spring '08 term at Cornell University (Engineering School).

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sol8 - Introduction to Algorithms CS 482, Spring 2008...

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