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- W4295200555 abstract "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 $Omega(n^{4/3})$ 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." @default.
- W4295200555 created "2022-09-12" @default.
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- W4295200555 date "2018-01-15" @default.
- W4295200555 modified "2023-09-25" @default.
- W4295200555 title "Searching for Maximum Out-Degree Vertices in Tournaments" @default.
- W4295200555 doi "https://doi.org/10.48550/arxiv.1801.04702" @default.
- W4295200555 hasPublicationYear "2018" @default.
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