By Dennis Komm
This textbook explains on-line computation in several settings, with specific emphasis on randomization and suggestion complexity. those settings are analyzed for numerous on-line difficulties comparable to the paging challenge, the k-server challenge, activity store scheduling, the knapsack challenge, the bit guessing challenge, and difficulties on graphs.
This publication is acceptable for undergraduate and graduate scholars of laptop technological know-how, assuming a simple wisdom in algorithmics and discrete arithmetic. additionally researchers will locate this a worthy reference for the hot box of recommendation complexity.
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Additional resources for An Introduction to Online Computation: Determinism, Randomization, Advice
Since Rand is optimal, it also has to be optimal in this (admittedly rather unlikely) case of “random” choices. Therefore, Alg is also optimal; moreover, we note that, for any fixed input length ????, Alg is one of the strategies in strat(Rand, ????). As a consequence, if we show that there is no optimal deterministic online algorithm for some online problem, we can conclude that there also is no optimal randomized one. It is very important to note that the above argument only holds for optimality, and that there is no analogous argument for 1-competitive randomized online algorithms.
In other words, is this the best we can hope for or are there online algorithms which outperform Fifo, Fwf, and Lru? The answer is that there is nothing better from a worst-case point of view. This means that, for every online algorithm Alg, there are infinitely many instances of paging for which Alg’s cost is at least ???? times larger than the optimal cost. To 21 Chapter 1. Introduction model such hard instances, we think of an adversary that constructs a hard instance ???? while knowing the online algorithm Alg we want to analyze.
In what follows, we will study an online algorithm that is allowed to remove some pages from the cache without loading other pages into it. Show that also such an algorithm can be converted into a demand paging algorithm without increasing its cost. Again, the cost measurement has to be changed. Here, the removal of a page from the cache is free, while loading a page into the cache causes cost 1. As already mentioned, an (online) algorithm for paging is basically defined by the strategy that it follows when a page fault occurs and a page in its cache (the victim page) needs to be replaced.
An Introduction to Online Computation: Determinism, Randomization, Advice by Dennis Komm