动态选择问题的鲁棒在线算法
Robust Online Algorithms for Dynamic Choosing Problems
摘要：
允许执行有界数量的重新打包的半在线算法在更现实的设置中实现保证良好的最坏情况行为。以前的大多数工作集中在最小化问题，旨在最大限度地减少一些成本。在这项工作中，我们研究的最大化问题，旨在最大限度地提高他们的利润。我们主要关注一类我们称之为选择问题的问题，其中必须维护一组对象的最大利润子集。许多已知的问题，如背包，MaximumIndependentSet及其变体，都是该类的一部分。我们提出了一个框架，选择问题，使我们能够转移到$(α-epsilon)$的离线$α$ -近似算法竞争半在线算法分期迁移$O(1/ε)$。此外，我们补充这些积极的结果与下界，表明我们的结果是紧密的意义上说，没有摊销迁移的$o(1/ε)$是可能的。
英文摘要：
Semi-online algorithms that are allowed to perform a bounded amount of repacking achieve guaranteed good worst-case behaviour in a more realistic setting. Most of the previous works focused on minimization problems that aim to minimize some costs. In this work, we study maximization problems that aim to maximize their profit. We mostly focus on a class of problems that we call choosing problems, where a maximum profit subset of a set objects has to be maintained. Many known problems, such as Knapsack, MaximumIndependentSet and variations of these, are part of this class. We present a framework for choosing problems that allows us to transfer offline $α$-approximation algorithms into $(α-epsilon)$-competitive semi-online algorithms with amortized migration $O(1/ε)$. Moreover we complement these positive results with lower bounds that show that our results are tight in the sense that no amortized migration of $o(1/ε)$ is possible.
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