Download An Introduction to Online Computation: Determinism, by Dennis Komm PDF

By Dennis Komm

This textbook explains on-line computation in numerous settings, with specific emphasis on randomization and suggestion complexity. those settings are analyzed for numerous on-line difficulties corresponding to the paging challenge, the k-server challenge, activity store scheduling, the knapsack challenge, the bit guessing challenge, and difficulties on graphs.

This e-book 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 invaluable reference for the hot box of recommendation complexity.

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Extra resources for An Introduction to Online Computation: Determinism, Randomization, Advice

Example text

This makes it very easy for us to argue why such an algorithm makes at most ???? page faults in one phase. 25 Chapter 1. 8. Every marking algorithm is strictly ????-competitive for paging. Proof. Let Mark be a fixed marking algorithm; let ???? denote the given input and consider its ????-phase partition into ???? phases ????1 , ????2 , . . 8. 4, we conclude that any optimal algorithm Opt makes at least ???? page faults in total on ????. What remains to be done is to show that Mark makes at most ???? page faults in one fixed phase ???????? with 1 ≤ ???? ≤ ???? .

The expected cost of Rand is therefore (︂ )︂ 1 1 · ???????? + 1 − ·1≤1+????.

To this end, we note that every deterministic strategy is chosen with a probability that is a multiple of 1/2????(????) . Now let ???? ∈ {1, 2, . . , 2????(????) }; instead of choosing a deterministic algorithm with a probability of ????/2????(????) , we can just choose ???? identical deterministic algorithms with a probability of 1/2????(????) each. This leads to the following observation. 2. Every randomized online algorithm Rand that uses at most ????(????) random bits for inputs of length ???? can be viewed as a set strat(Rand, ????) = {????1 , ????2 , .

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