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：给定一个从玩家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，每一对具有共同父节点的玩家相互竞争，胜者晋级至该共同父节点；随后，叶子节点被移除。当仅剩一名玩家时，该玩家被宣布为获胜者。这是体育赛事、选举和决策中广泛使用的竞赛形式。过去十年间，学界从理论与实践角度对此进行了深入研究。最常见的优化目标是设计种子编排以“帮助”（甚至确保）特定玩家赢得比赛。我们提出了一个从竞赛组织者视角更具实际意义的新目标：最大化赛事收益或受欢迎程度。具体而言，我们为每场可能发生的比赛赋予"分值"，并力求通过种子编排使实际进行比赛的得分总和最大化。我们聚焦于玩家实力存在全序关系的场景，并就该问题的计算复杂度给出了广泛的理论结果。