Dennis Komm's An Introduction to Online Computation: Determinism, PDF
By Dennis Komm
This textbook explains on-line computation in numerous settings, with specific emphasis on randomization and recommendation complexity. those settings are analyzed for numerous on-line difficulties resembling the paging challenge, the k-server challenge, task store scheduling, the knapsack challenge, the bit guessing challenge, and difficulties on graphs.
This e-book is acceptable for undergraduate and graduate scholars of desktop technology, assuming a uncomplicated wisdom in algorithmics and discrete arithmetic. additionally researchers will locate this a important reference for the new box of recommendation complexity.
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Additional resources for An Introduction to Online Computation: Determinism, Randomization, Advice
In every time step, Lifo causes a page fault while there is an optimal solution Opt(????) that removes a page ???????? with ???? ̸= ???? in time step ????1 and has cost 1 overall, because it has ???????? and ????????+1 in its cache from that point on. So we see that there is a significant difference between Fifo and Lifo. This is not very surprising; intuitively it seems like a bad idea to immediately remove a page from the cache that was just loaded into it. What about Lfu? Here, an intuitive point of view might suggest more success; we learn from what happened so far, namely, we replace a page that was in some sense the least valuable up to now.
1 , ????2 , ????2 , . . , ????2 , . . , ????????−1 , ????????−1 , . . , ????????−1 , ????????+1 , ???????? , . . , ????????+1 , ???????? ) ⏟ ⏞ ⏟ ⏞ ⏟ ⏞ ⏟ ⏞ ????′ requests ????′ requests ????′ requests 2(????′ −1) requests of length ???? := (????−1)????′ +2(????′ −1). In the first (????−1)????′ time steps, no online algorithm causes a page fault, and after that, all pages in the cache have been requested ????′ times except for ???????? . Thus, when ????????+1 is requested in time step ????(????−1)????′ +1 , Lfu removes ???????? , which is the page in the cache that was used least frequently.
In other words, we do not want that there are some instances of the given problem that always cause an online algorithm to perform poorly; even if our feeling is that these inputs do not occur very often. ” With this in mind, we use the following approach to enable online algorithms to obtain a higher output quality, that is, to overcome the drawback of not knowing the future, at least to some extent. We allow the online algorithm at hand to base its computations on randomness. So far, the output of a fixed algorithm was fully determined by its strategy and the input, which is why we call such algorithms deterministic online algorithms.
An Introduction to Online Computation: Determinism, Randomization, Advice by Dennis Komm