Complexity of Online Algorithms - CSIS
Complexity of Online Algorithms - CSIS
Complexity of Online Algorithms - CSIS
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Paging against an oblivious adversary<br />
Theorem:<br />
• Let R be a randomized online algorithm for paging. Then<br />
C R<br />
obl<br />
>= H k where H k is k th Harmonic number.<br />
Pro<strong>of</strong>:<br />
• We will use Yao’s minimax principle i.e.<br />
• we will choose a probability distribution and<br />
• find the best performance for it by a deterministic online<br />
algorithm<br />
• which will be the lower bound for the performance <strong>of</strong> any<br />
randomized online algorithm<br />
• Let I = { I 1 , I 2 , ..., I k+1 } be the set <strong>of</strong> possible pages to be<br />
requested.<br />
• We will construct a probability distribution p on request<br />
sequences <strong>of</strong> length N >= k<br />
• and prove that for p the best expected performance by a<br />
deterministic online algorithm is H k .
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