在线图探索的4的下界
A lower bound of 4 for online graph exploration
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中文总结 AI 辅助
研究在线图探索问题，通过证明对智能体行为施加限制不影响竞争比，得出该问题竞争比至少为4，改进了此前10/3的最好下界，还表明某些图属性可在不影响竞争比时被假设。
中文摘要 AI 辅助
在在线图探索问题中，单个智能体需要访问一个初始未知的图的每个顶点，该图随着时间以在线方式被了解，然后回到起始位置。我们证明了这个问题的竞争比至少为4，改进了之前已知的最好下界10/3。我们证明的一个关键要素是表明可以对智能体的行为施加一些限制而不影响竞争比。作为副产品，我们还得出某些图属性，如三角不等式或次立方性，可以在不影响竞争比的情况下被假设。
英文摘要
In the online graph exploration problem, a single agent needs to visit every vertex of an initially unknown graph, which is learned over time in an online fashion, and return to its starting position. We prove that the competitive ratio of this problem is at least 4, improving on the previously best known lower bound of 10/3. A key ingredient of our proof is showing that several restrictions can be imposed on the agent's behavior without affecting the competitive ratio. As a byproduct, we also obtain that certain graph properties, such as the triangle inequality or being subcubic, can be assumed without affecting the competitive ratio.
