The graph exploration problem asks a searcher to explore an unknown graph. This problem can be interpreted as the online version of the Traveling Salesman Problem. The treasure hunt problem is the corresponding online version of the shortest s-t-path problem. It asks the searcher to find a specific vertex in an unknown graph at which a treasure is hidden. Recently, the analysis of the impact of a priori knowledge is of interest. In graph problems, one form of a priori knowledge is a map of the graph. We survey the graph exploration and treasure hunt problem with an unlabeled map, which is an isomorphic copy of the graph, that is provided to the searcher. We formulate decision variants of both problems by interpreting the online problems as a game between the online algorithm (the searcher) and the adversary. The map, however, is not controllable by the adversary. The question is, whether the searcher is able to explore the graph fully or find the treasure for all possible decisions of the adversary. We prove the PSPACE-completeness of these games, whereby we analyze the variations which ask for the mere existence of a tour through the graph or path to the treasure and the variations that include costs. Additionally, we analyze the complexity of related problems that ask for a tour in the graph or a s-t path.

翻译：图探索问题要求搜索者探索一个未知图。该问题可被理解为旅行商问题的在线版本。寻宝问题则是最短s-t路径问题的在线对应问题，其要求搜索者在未知图中找到隐藏宝藏的特定顶点。近期，先验知识的影响分析备受关注。在图问题中，先验知识的一种形式是图的地图。我们研究了在提供无标签地图（即图的同构副本）情况下的图探索与寻宝问题。通过将在线问题解释为在线算法（搜索者）与对手之间的博弈，我们构建了这两个问题的决策变体。但地图不受对手控制。核心问题在于：搜索者能否针对对手的所有可能决策完成图的完全探索或找到宝藏？我们证明了这些博弈是PSPACE完全的，其中我们分析了要求图中存在遍历环或通往宝藏的路径的变体，以及包含代价的变体。此外，我们还分析了要求图中存在环或s-t路径的相关问题的复杂度。