Advice Complexity of Adaptive Priority Algorithms
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The priority model was introduced by Borodin, Rackoff and Nielsen to capture "greedy-like" algorithms. Motivated, in part, by the success of advice complexity in the area of online algorithm, recently Borodin et al. have extended the fixed priority model to include an advice tape oracle. They also developed a reduction-based framework for proving lower bounds against this rather powerful model. In this paper, we extend the advice tape model further to the arguably more useful adaptive priority algorithms. We show how to modify the reduction-based framework in order for it to apply against the more powerful adaptive priority algorithms. In the process, we manage to simplify the proof that the framework works, and we strengthen all the lower bounds by a factor of 2. As a motivation of an adaptive priority model with advice, we present a purely combinatorial adaptive priority algorithm with advice for the minimum vertex cover problem on graphs of maximum degree 3. Our algorithm achieves optimality and uses at most 15n/46 bits of advice. This advice is provably shorter than what can be achieved by online algorithms with advice.
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