Related papers: Maps of Tournaments: Distances, Experiments, and D…
We consider the manipulability of tournament rules which map the results of $\binom{n}{2}$ pairwise matches and select a winner. Prior work designs simple tournament rules such that no pair of teams can manipulate the outcome of their match…
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
So-called battle maps are an appropriate way to visually summarize the flow of battles as they happen in many team-based combat games. Such maps can be a valuable tool for retrospective analysis of battles for the purpose of training or for…
In a prediction tournament, contestants "forecast" by asserting a numerical probability for each of (say) 100 future real-world events. The scoring system is designed so that (regardless of the unknown true probabilities) more accurate…
The well-known three distance theorem states that there are at most three distinct gaps between consecutive elements in the set of the first n multiples of any real number. We generalise this theorem to higher dimensions under a suitable…
Seymour's distance two conjecture states that in any digraph there exists a vertex (a "Seymour vertex") that has at least as many neighbors at distance two as it does at distance one. We explore the validity of probabilistic statements…
In this paper we bring a novel approach to the theory of tournament rankings. We combine two different theories that are widely used to establish rankings of populations after a given tournament. First, we use the statistical approach of…
Recently, Szufa et al. [AAMAS 2020] presented a "map of elections" that visualizes a set of 800 elections generated from various statistical cultures. While similar elections are grouped together on this map, there is no obvious…
The theory of tournament limits and tournament kernels (often called graphons) is developed by extending common notions for finite tournaments to this setting; in particular we study transitivity and irreducibility of limits and kernels. We…
The score sequence of a tournament is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The problem of counting score sequences of a tournament with $n$ vertices is more than 100 years old (MacMahon 1920). In…
Decomposing a digraph into subdigraphs with a fixed structure or property is a classical problem in graph theory and a useful tool in a number of applications of networks and communication. A digraph is strongly connected if it contains a…
Distance transformation is an image processing technique used for many different applications. Related to a binary image, the general idea is to determine the distance of all background points to the nearest object point (or vice versa). In…
In the run-up to any major sports tournament, winning probabilities of participants are publicized for engagement and betting purposes. These are generally based on simulating the tournament tens of thousands of times by sampling from…
We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a…
Semantic mapping is the incremental process of "mapping" relevant information of the world (i.e., spatial information, temporal events, agents and actions) to a formal description supported by a reasoning engine. Current research focuses on…
A random walk-like model is considered to discuss statistical aspects of tournaments. The model is applied to soccer leagues with emphasis on the scores. This competitive system was computationally simulated and the results are compared…
A tournament is a method to decide the winner in a competition, and describes the overall sequence in which matches between the players are held. While deciding a worthy winner is the primary goal of a tournament, a close second is to…
Tournament solutions provide methods for selecting the "best" alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out…
A 2.75-approximation algorithm is proposed for the unconstrained traveling tournament problem, which is a variant of the traveling tournament problem. For the unconstrained traveling tournament problem, this is the first proposal of an…