Dynamic Programming Algorithms for Computing Optimal Knockout Tournaments
نویسندگان
چکیده
We study competitions structured as hierarchically shaped single-elimination tournaments. define optimal tournaments by maximizing attractiveness such that the topmost players will have chance to meet in higher stages of tournament. propose a dynamic programming algorithm for computing and we provide its sound complexity analysis. Based on idea approach, also develop more efficient deterministic stochastic sub-optimal algorithms. present experimental results obtained with Python implementation all proposed algorithms regarding optimality solutions efficiency running time.
منابع مشابه
Optimal seeding in knockout tournaments
Optimal seeding in balanced knockout tournaments has only been studied in very limited settings, for example, maximizing predictive power for up to 8 players using only the relative ranking of the players (ordinal information). We broaden the scope of the analysis along several dimensions: tournaments of size up to 128, different player models, ordinal as well as cardinal solutions, and two add...
متن کاملBayesian locally-optimal design of knockout tournaments
The elimination or knockout format is one of the most common designs for pairing competitors in tournaments and leagues. In each round of a knockout tournament, the losers are eliminated while the winners advance to the next round. Typically, the goal of such a design is to identify the overall best player. Using a common probability model for expressing relative player strengths, we develop an...
متن کاملDynamic Programming Algorithms for Efficiently Computing Cosegmentations between Biological Images
Algorithms for comparing trees have recently been found relevant in the context of bioimage analysis. While previously proposed algorithms deal with problems that are computationally hard in general, we propose efficient algorithms for restricted versions that are able to handle significantly larger instances in practice. We propose two dynamic programming algorithms for the so-called tree assi...
متن کاملBroadening the Scope of Optimal Seeding Analysis in Knockout Tournaments
Optimal seeding in balanced knockout tournaments has only been studied in very limited settings, for example, maximizing predictive power for up to 8 players using only the relative ranking of the players (ordinal information). We dramatically broaden the scope of the analysis along several dimensions. First, we propose a heuristic algorithm that makes use of available cardinal information and ...
متن کاملOptimal effort incentives in dynamic tournaments
This paper analyzes two-stage rank-order tournaments. A principal decides (i) how to spread prize money across the two periods, (ii) how to weigh performance in the two periods when awarding the second-period prize, and (iii) whether to reveal performance after the first period. The information revelation policy depends exclusively on properties of the effort cost function. The principal always...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2021
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math9192480