CSC 7103 20091008

# CSC 7103 20091008 - f are all overloaded. We dont know...

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CSC 7103 10/8/2009 Page 1 of 2 Type up notes from notepad. Claim : SF A (σ) has a competitive ratio of 2 and doesn’t fail. M is # of machines, N is # of jobs Proof : We must show that if you keep following the algorithm, then by the time you got to the last job, you would be able to assign that job to a machine. Consider jobs r 1 , r 2 , …, r N-1 , r N At the last job we must show there is no machine that fits the criteria for the algorithm (in choosing the machine). We divide the set of machines into two sets, one of lightly loaded machines and one of heavily loaded machines. Figure 1 – machine split Let f be the index of the fastest machine whose load l N-1 (f) <= OPT(σ) <= A. What can we say about l N-1 (M)? We must show that if f exists, f must be < M and all nodes after M

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Unformatted text preview: f are all overloaded. We dont know anything about the load of nodes before M f . Figure 2 machine knowledge B = { i | i &gt; f } C = { all other machines not in B } S i = Set of jobs assigned to machine by slow fit to machine i in the set B S i * = Set of jobs assigned to machine by OPT() to machine i in the set B If S i * = S i , then OPT behaved the same as slow fit, so we need to show there is a difference in the sets. Suppose B = { 1, 2, , M , then all machines are overloaded and this is undesirable. To show that f exists we must show that B is not the set of all machines. Proof of slow fit algorithm CSC 7103 10/8/2009 Page 2 of 2 Static scheduling...
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## CSC 7103 20091008 - f are all overloaded. We dont know...

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