A tournament is a complete graph with its edges directed, and colouring a tournament means partitioning its vertex set into transitive subtournaments. For some tournaments H there exists c such that every tournament not containing H as a subtournament has chromatic number at most c (we call such a tournament H a hero); for instance, all tournaments with at most four vertices are heroes. In this...

We observe that ranking systems—a theoretical framework for web page ranking and collaborative filtering introduced by Altman and Tennenholtz—and tournament solutions—a well-studied area of social choice theory—are strongly related. This relationship permits a mutual transfer of axioms and solution concepts. As a first step, we formally analyze a tournament solution that is based on Google’s Pa...

Tournament selection is one of the most popular selection operators in Genetic Algorithms. Recently, its popularity is increasing because this operator is well suited for Parallel Genetic Algorithms applications. In this paper, new selection operator is proposed. The new operator, which should be an improvement of the tournament selection, is named “Fine-grained Tournament Selection” (FGTS). It...

The task of understanding the dynamics of coevolutionary algorithms or comparing performance between such algorithms is complicated by the fact the internal fitness measures are subjective. Though several techniques have been proposed to use external or objective measures to help in analysis, there are clearly properties of fitness payoff, like intransitivity, for which these techniques are ine...

How Many Winners Are Good to Have? On Tournaments with Sabotage From an employer’s perspective a tournament should induce agents to exert productive activities but refrain from destructive ones. We experimentally test the predictive power of a tournament model which suggests that – within a reasonable framework – productive and destructive activities are not influenced neither by the number of ...

In this paper, we motivate and describe a term long game tournament. The tournament has different milestones, including breadth first search, heuristic search, knowledge representation and reasoning and the tournament proper. For this last milestone, students are encouraged to use machine learning techniques. We describe in detail each of the milestones as well as the game and its specification...

Knockout tournaments are very common in practice for various settings such as sport events and sequential pairwise elimination elections. In this paper, we investigate the computational aspect of tournament agenda control, i.e., finding the agenda that maximizes the chances of a target player winning the tournament. We consider several modelings of the problem based on different constraints tha...

It is well known that every tournament has a directed path containing all the vertices of V , i.e. a hamiltonian path. It is an easy exercise to show that a tournament has a unique such path if and only if the arcs of A induce a transitive relation on V . In this paper we show that by reversing the arcs of the hamiltonian path in a transitive tournament with n vertices we obtain a tournament wi...

We analyze tournaments of heterogeneous players from an organizer’s perspective. Using a simple model of a noisy tournament, we demonstrate how the likelihood of selecting the best player, here termed the “predictive power” of a tournament, depends on the tournament format, the distribution of players’ types, and the overall noise level. We formalize the organizer’s decision problem for varying...

Our work investigates the problem of retrieving the maximum item from a set in crowdsourcing environments. We focus on tournament algorithms that can for instance select the best Facebook profile that matches a given person or the best photo that describes a given restaurant. Tournament algorithms can be tuned with parameters such as the desired difference of votes between the top-2 voted outco...