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Searching for Maximum Out-Degree Vertices in Tournaments
- Publication Year :
- 2018
-
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.
- Subjects :
- Computer Science - Data Structures and Algorithms
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1801.04702
- Document Type :
- Working Paper