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• W2953102761 abstract "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 $logleft(1+(c-1)^{c-1}/c^{c}right)n=Theta (n/c)$ bits of advice are necessary and sufficient (up to an additive term of $O(log n)$) to achieve a competitive ratio of $c$. The results are obtained by introducing a new string guessing problem related to those of Emek et al. (TCS 2011) and Bockenhauer et al. (TCS 2014). It turns out that this gives a powerful but easy-to-use method for providing both upper and lower bounds on the advice complexity of an entire class of online problems, the AOC-complete problems. Previous results of Halld'orsson et al. (TCS 2002) on online independent set, in a related model, imply that the advice complexity of the problem is $Theta (n/c)$. Our results improve on this by providing an exact formula for the higher-order term. For online disjoint path allocation, Bockenhauer et al. (ISAAC 2009) gave a lower bound of $Omega (n/c)$ and an upper bound of $O((nlog c)/c)$ on the advice complexity. We improve on the upper bound by a factor of $log c$. For the remaining problems, no bounds on their advice complexity were previously known." @default.
• W2953102761 created "2019-06-27" @default.
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• W2953102761 date "2014-08-29" @default.
• W2953102761 modified "2023-09-27" @default.
• W2953102761 title "The Advice Complexity of a Class of Hard Online Problems" @default.
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