Online computation is a concept to model uncertainty where not all information on a problem instance is known in advance. An online algorithm receives requests which reveal the instance piecewise and has to respond with irrevocable decisions. Often, an adversary is assumed that constructs the instance knowing the deterministic behavior of the algorithm. From a game theoretical point of view, the adversary and the online algorithm are players in a two-player game. By applying this view on combinatorial graph problems, especially on problems where the solution is a subset of the vertices, we analyze their complexity. For this, we introduce a framework based on gadget reductions from 3-Satisfiability and extend it to an online setting where the graph is a priori known by a map. This is done by identifying a set of rules for the reductions and providing schemes for gadgets. The extension of the framework to the online setting enable reductions from TQBF. We provide example reductions to the well-known problems Vertex Cover, Independent Set and Dominating Set and prove that they are PSPACE-complete. Thus, this paper establishes that the online version with a map of NP-complete graph problems form a large class of PSPACE-complete problems.
翻译：在线计算是模拟不确定性的概念, 并不是所有关于问题实例的信息都是事先知道的。 在线算法会收到显示该实例的请求, 并且必须做出不可撤销的决定。 通常, 对手会假设该实例是了解算法的决定性行为。 从游戏的理论观点看, 对手和在线算法是双玩家游戏中的玩家。 在组合图问题上应用这种观点, 特别是当解决问题的方法是顶端的一个子项时, 我们分析其复杂性。 为此, 我们引入了一个基于3- 满意度的缩放技术框架, 并将其扩展至地图上先行显示该图的在线设置。 这样做的方法是确定一套削减规则, 并提供工具。 将框架扩展至在线设置可以减少 TQBFFF 。 我们为众所周知的问题“ Vetex Cover, 独立设置和确定其复杂性 ”, 并证明这些问题是 PCACE 的完整 。 因此, 本文将在线版本与 PP- compreal gration plas proma problement proma mass problear problear pass problear pass pass pass pass pass problem problem problem probleglem 。
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