This House Proves that Debating is Harder than Soccer

During the last twenty years, a lot of research was conducted on the sport elimination problem: Given a sports league and its remaining matches, we have to decide whether a given team can still possibly win the competition, i.e., place first in the league at the end. Previously, the computational complexity of this problem was investigated only for games with two participating teams per game. In this paper we consider Debating Tournaments and Debating Leagues in the British Parliamentary format, where four teams are participating in each game. We prove that it is NP-hard to decide whether a given team can win a Debating League, even if at most two matches are remaining for each team. This contrasts settings like football where two teams play in each game since there this case is still polynomial time solvable. We prove our result even for a fictitious restricted setting with only three teams per game. On the other hand, for the common setting of Debating Tournaments we show that this problem is fixed parameter tractable if the parameter is the number of remaining rounds $k$. This also holds for the practically very important question of whether a team can still qualify for the knock-out phase of the tournament and the combined parameter $k + b$ where $b$ denotes the threshold rank for qualifying. Finally, we show that the latter problem is polynomial time solvable for any constant $k$ and arbitrary values $b$ that are part of the input.Comment: 18 pages, to appear at FUN 201

Spartan Daily, October 31, 1941

Volume 30, Issue 27https://scholarworks.sjsu.edu/spartandaily/3347/thumbnail.jp

Xavier University Newswire

https://www.exhibit.xavier.edu/student_newspaper/1666/thumbnail.jp

The Trinity Ivy, 1941

Student Yearbook for Trinity College, Hartford Connecticuthttps://digitalrepository.trincoll.edu/ivy/1037/thumbnail.jp

Spartan Daily, December 3, 1980

Volume 75, Issue 64https://scholarworks.sjsu.edu/spartandaily/6699/thumbnail.jp

Lanthorn, vol. 25, no. 06, October 3, 1990

Lanthorn is Grand Valley State\u27s student newspaper, published from 1968 to the present