A Connection Between Sports and Matroids: How Many Teams Can We Beat?

Schlotter, Ildikó; Cechlárová, Kataŕına

doi:10.1007/s00453-016-0256-2

Cited by 4 publications

(5 citation statements)

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“…A first application of linear programming to the same problem was published by Robinson (1991). The computational complexity of determining the best and worst possible final rank of a team, among other related questions, is discussed in Schlotter and Cechlárová (2018) and Gusfield and Martel (2002). In Raack et al (2014) a general ranking integer programming model that calculates the number of points that is needed to finish ith in any sport, including football, motor sports and ice hockey is developed.…”

Section: Introductionmentioning

confidence: 99%

Bounding the final rank during a round robin tournament with integer programming

Gotzes

Hoppmann

2020

Oper Res Int J

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This article is mainly motivated by the urge to answer two kinds of questions regarding the Bundesliga, which is Germany's primary football (soccer) division having the highest average stadium attendance worldwide: "At any point in the season, what is the lowest final rank a certain team can achieve?" and "At any point in the season, what is the highest final rank a certain team can achieve?". Although we focus on the Bundesliga in particular, the integer programming formulations we introduce to answer these questions can easily be adapted to a variety of other league systems and tournaments.

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Section: Introductionmentioning

confidence: 99%

Bounding the final rank during a round robin tournament with integer programming

Gotzes

Hoppmann

2020

Oper Res Int J

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“…What holds true is that Independent Set is W[1]-hard on K 1,4 -free graphs, as proved by Hermelin, Mnich, and Van Leeuwen [1]. So the term "claw-free" in the above statement (Theorem 3 of our article [4]) should be replaced by "K 1,4 -free".…”

Section: The Error and Its Correctionmentioning

confidence: 86%

“…In Theorem 3 of our article [4], we incorrectly stated that "MinStanding(S) is W[1]-hard with parameter |V (G)| − r for any well-based set S of outcomes, even if the (undirected version of the) input graph G is claw-free". The presented (erroneous) proof gave an FPT reduction from the W[1]-hard Independent Set problem.…”

Section: The Error and Its Correctionmentioning

confidence: 99%

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Correction to: A Connection Between Sports and Matroids: How Many Teams Can We Beat?

Schlotter

Cechlárová

2017

Algorithmica

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BackgroundOur article "A connection between sports and matroids: How many teams can we beat?" [4] deals with a problem we called MinStanding(S). The motivation behind this problem comes from the following situation. Given an ongoing sports competition among a set T of teams, with each team having a current score and some matches left to be played, we ask whether it is possible for our distinguished team t ∈ T to obtain a final standing with at most r teams finishing before t.For a general model that can be applied to various sports competitions, we denoted by S the set of all possible outcomes of a match, where each outcome is a pair ( p 1 , p 2 ) of non-negative reals corresponding to the situation where the match ends with the home team obtaining p 1 points and the away team obtaining p 2 points. If S contains pairs (α, 0) and (0, β) for some positive α and β, then we say that S is well based.Given a set S of outcomes with |S| = k + 1, the above question boils down to the following graph labelling problem:The online version of the original article can be found under

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“…In a subsequent article [166], we also investigated the complexity of the following generalization of GSE(S): given the current situation in an on-going sports competition, we ask whether it is possible for our distinguished team T to obtain a final standing with at most r teams finishing before T. We studied the computational complexity of this problem, addressing it both from the viewpoint of parameterized complexity and of approximation. We focused on a special case equivalent to finding a maximal induced subgraph of a given graph G that admits an orientation where the in-degree of each vertex is upper-bounded by a given function.…”

Section: The Sports Elimination Problem From a Computational Viewmentioning

confidence: 99%

BME VIK Annual Research Report on Electrical Engineering and Computer Science 2016

Charaf

Harsányi

Poppe

et al. 2017

Period. Polytech. Elec. Eng. Comp. Sci.

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Preface Since being established in 1949, the Faculty of Electrical Engineering and Informatics (VIK) BME has played a flagship role in the development of electronics, IT and computer science in Hungary.We László Jakab (dean, BME VIK) János Levendovszky (vice-dean in charge of scientific affairs, BME VIK) are proud of combining engineering applications with sound scientific results, which is the assurance of high-level industrial collaboration leading to novel results and innovation. The various collaborations with our industrial partners has made it clear that the industry expects methods and results which make their industrial processes more effective and increase productivity and quality. Thus, participation in these collaborations give a competitive edge and ensure the continuous development of VIK. These factors have positioned our Department of Automation and Applied InformaticsDepartment of Automation and Applied Informatics (AUT) is one of the largest and dynamically developing departments at BME with diverse scope competences such as control theory, embedded systems, software modelling, applied software development, Internet of Things, power electronics, mechatronics, and many others. The department's main activities are education, research and development. Training versatile electrical and software engineers with solid practical knowledge is our top priority. Our profile also includes developing high quality software and hardware solutions for industry partners. All of our activities are backed by strong research background.In 2016, the department organized and hosted a number of domestic and international events. In cooperation with the industry, AUT has organized the IoT4U conference. It was dedicated to Internet of Things, cloud and data management as well as the integration of IoT into various formats. RobonAUT, the yearly domestic amateur robotics contest was organized by the department in February 2016. The yearly contest is open to teams of students, organized either in student projects within the department or independent research teams.The next sections summarize the key research results of the department in year 2016. Software Development Methods and Mobile PlatformsThe diversity of mobile platforms necessitates the development of the same mobile application for all major mobile platforms, what requires considerable development effort. Mobile application developers are multiplatform developers, but they still prioritize the platforms, therefore, not all platforms are equally important for them. Appropriate methods, processes and tools are required to support the development in order to achieve better productivity.The research on educational mobile applications that adapt to the mental state of the user required a method for estimating the difficulty of tasks found in the serious games. There are generated or random assignments where the effort required from the user is not known or cannot be estimated in advance.61 (2) IoT and Smart CityThe Internet of Things (IoT) is transforming the surroun...

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A Connection Between Sports and Matroids: How Many Teams Can We Beat?

Cited by 4 publications

References 25 publications

Bounding the final rank during a round robin tournament with integer programming

Bounding the final rank during a round robin tournament with integer programming

Correction to: A Connection Between Sports and Matroids: How Many Teams Can We Beat?

BME VIK Annual Research Report on Electrical Engineering and Computer Science 2016

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