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 varied on-line difficulties similar to 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 suitable for undergraduate and graduate scholars of desktop technological know-how, assuming a simple wisdom in algorithmics and discrete arithmetic. additionally researchers will locate this a helpful reference for the hot box of recommendation complexity.
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Additional resources for An Introduction to Online Computation: Determinism, Randomization, Advice
The way we measure the solution quality of algorithms, such an algorithm is considered bad. 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.
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. 1. Consider the following online minimization problem, for which we have an almost optimal randomized online algorithm, but for which any deterministic online algorithm is very bad.
94]. The Christofides algorithm for the TSP was introduced in 1976 by Christofides . Competitive analysis was introduced in 1985 by Sleator and Tarjan . 18 that makes use of resource augmentation); the authors also showed that Lru is ????-competitive. 12) is an optimal offline algorithm for paging . The terms competitive and strongly competitive were first used in this context by Karlin et al. . “Online Computation and Competitive Analysis” from Borodin and El-Yaniv  is certainly the standard textbook on online algorithms and gives both a broad and deep introduction to the topic.