Given a mapping from a set of players to the leaves of a complete binary tree (called a seeding), a knockout tournament is conducted as follows: every round, every two players with a common parent compete against each other, and the winner is promoted to the common parent; then, the leaves are deleted. When only one player remains, it is declared the winner. This is a popular competition format in sports, elections, and decision-making. Over the past decade, it has been studied intensively from both theoretical and practical points of view. Most frequently, the objective is to seed the tournament in a way that "assists" (or even guarantees) some particular player to win the competition. We introduce a new objective, which is very sensible from the perspective of the directors of the competition: maximize the profit or popularity of the tournament. Specifically, we associate a "score" with every possible match, and aim to seed the tournament to maximize the sum of the scores of the matches that take place. We focus on the case where we assume a total order on the players' strengths, and provide a wide spectrum of results on the computational complexity of the problem.

翻译：给定一个从选手集合到完全二叉树叶子节点的映射（称为种子编排），淘汰赛按以下方式进行：每轮比赛中，具有共同父节点的两名选手相互竞争，胜者晋级至该共同父节点；随后，叶子节点被删除。当仅剩一名选手时，该选手即被宣布为获胜者。这是体育赛事、选举及决策过程中广受欢迎的竞赛形式。过去十年间，学界从理论与应用两个维度对其展开了深入研究。常见的研究目标是通过种子编排策略"协助"（甚至确保）特定选手赢得比赛。我们提出一个符合赛事组织者视角的新目标：最大化赛事收益或受欢迎程度。具体而言，我们为每场潜在比赛赋予"分值"，旨在通过种子编排使所有实际发生比赛的分值总和最大化。我们重点研究选手实力存在全序关系的情形，并就该问题的计算复杂度提供了一系列广泛结论。