Online algorithms with advice is an area of research where one attempts to measure how much knowledge of the future is necessary to achieve a given competitive ratio. The lower bound results give robust bounds on what is possible using semi-online algorithms. On the other hand, when the advice is of an obtainable form, algorithms using advice can lead to semi-online algorithms. There are strong relationships between advice complexity and randomization, and advice complexity has led to the introduction of the first complexity classes for online problems.
This survey concerning online algorithms with advice explains the models, motivates the study in general, presents some examples of the work that has been carried out, and includes a fairly complete set of references, organized by problem studied.
The advice complexity of an online problem is a measure of how much knowledge of the future an online algorithm needs in order to achieve a certain competitive ratio. Using advice complexity, we define the first online complexity class, AOC. The class includes independent set, vertex cover, dominating set, and several others as complete problems. AOC-complete problems are hard, since a single wrong answer by the online algorithm can have devastating consequences. For each of these problems, we show that log 1 + (c − 1) c−1 /c c n = Θ (n/c) bits of advice are necessary and sufficient (up to an additive term of O(log n)) to achieve a competitive ratio of c. on the upper bound by a factor of log c. For the remaining problems, no bounds on their advice complexity were previously known.
Abstract. The online search problem is a fundamental problem in finance. The numerous direct applications include searching for optimal prices for commodity trading and trading foreign currencies. In this paper, we analyze the advice complexity of this problem. In particular, we are interested in identifying the minimum amount of information needed in order to achieve a certain competitive ratio. We design an algorithm that reads b bits of advice and achieves a competitive ratio of (M/m) 1/(2 b +1) where M and m are the maximum and minimum price in the input. We also give a matching lower bound. Furthermore, we compare the power of advice and randomization for this problem.
In online scenarios requests arrive over time, and each request must be serviced in an irrevocable manner before the next request arrives. Online algorithms with advice is an area of research where one attempts to measure how much knowledge of future requests is necessary to achieve a given performance level, as defined by the competitive ratio. When this knowledge, the advice, is obtainable, this leads to practical algorithms, called semi-online algorithms. On the other hand, each negative result gives robust results about the limitations of a broad range of semi-online algorithms. This survey explains the models for online algorithms with advice, motivates the study in general, presents some examples of the work that has been carried out, and includes an extensive set of references, organized by problem studied.
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