知识状态算法：有限信息的随机化
Knowledge State Algorithms: Randomization with Limited Information
摘要：
我们引入了知识状态的概念，许多著名的算法可以被视为知识状态算法。知识状态方法可以用来构造竞争性随机在线算法，研究竞争性和记忆之间的权衡。一个知识状态只是通过固定一个工作函数来简单地陈述对手的条件义务，并给出算法的分布。当知识状态算法接收到请求时，它然后计算一个或多个“后续”知识状态，以及转换到每个状态的概率。然后，该算法使用随机化来选择其中一个作为新的知识状态。我们应用该方法的分页问题。我们提出了最优竞争算法的情况下，缓存大小为k=2和k=3的分页。这些算法只使用非常有限数量的书签。
英文摘要：
We introduce the concept of knowledge states; many well-known algorithms can be viewed as knowledge state algorithms. The knowledge state approach can be used to to construct competitive randomized online algorithms and study the tradeoff between competitiveness and memory. A knowledge state simply states conditional obligations of an adversary, by fixing a work function, and gives a distribution for the algorithm. When a knowledge state algorithm receives a request, it then calculates one or more "subsequent" knowledge states, together with a probability of transition to each. The algorithm then uses randomization to select one of those subsequents to be the new knowledge state. We apply the method to the paging problem. We present optimally competitive algorithm for paging for the cases where the cache sizes are k=2 and k=3. These algorithms use only a very limited number of bookmarks.
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