旅游地图中最大出度顶点的搜索
Searching for Maximum Out-Degree Vertices in Tournaments
摘要：
如果对于$T$的每个顶点$y$，存在从$x$到$y$的长度至多为2的有向路径，则竞赛图$T$中的顶点$x$被称为王。不难证明，在一个竞赛图中，每一个最大出度的顶点都是王。然而，竞赛图可能有国王不是最大出度的顶点。二进制查询询问一对顶点之间的边的方向并接收答案。在未知的锦标赛中找到一个国王的成本是检测国王所需的二进制查询的数量。对于在锦标赛中寻找国王的成本，在最坏的情况下，沉，盛和吴（SIAM J.Comput.，2003）分别证明了$Ω(n^{4/3})$和$O(n^{3/2})$的上下界。与他们的结果相反，我们证明了在最坏的情况下，找到最大出度顶点的代价是${n \choose 2} -O(n)$。
英文摘要：
A vertex $x$ in a tournament $T$ is called a king if for every vertex $y$ of $T$ there is a directed path from $x$ to $y$ of length at most 2. It is not hard to show that every vertex of maximum out-degree in a tournament is a king. However, tournaments may have kings which are not vertices of maximum out-degree. A binary inquiry asks for the orientation of the edge between a pair of vertices and receives the answer. The cost of finding a king in an unknown tournament is the number of binary inquiries required to detect a king. For the cost of finding a king in a tournament, in the worst case, Shen, Sheng and Wu (SIAM J. Comput., 2003) proved a lower and upper bounds of $Ω(n^{4/3})$ and $O(n^{3/2})$, respectively. In contrast to their result, we prove that the cost of finding a vertex of maximum out-degree is ${n \choose 2} -O(n)$ in the worst case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
