Knockout tournaments provide a common and important framework for structuring sporting competitions, worth billions of dollars every year in the global economy. Knockout tournaments also model a specific type of election scheme: namely, sequential pairwise elimination elections. The designer of a tournament typically controls both the shape of the tournament (usually a binary tree) and the seed...

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 power law with an exponent close to unity if the competitiveness is a stable quantity and a decisive factor to win a match. Otherwise, the distribution is fou...

This paper provides nested sets and vector representations of knockout tournaments. The paper introduces classification of probability domain assumptions and a new set of axioms. Two new seeding methods are proposed: equal gap seeding and increasing competitive intensity seeding. Under different probability domain assumptions, several axiomatic justifications are obtained for equal gap seeding....

In this paper we analyze the robustness of sorting and tournament algorithms against faulty comparisons. Sorting algorithms are differently affected by faulty comparisons depending on how comparison errors can affect the overall result. In general, there exists a tradeoff between the number of comparisons and the accuracy of the result, but some algorithms like Merge Sort are Pareto-dominant ov...

The paper analyses how draw constraints influence the outcome of a knockout tournament. research question is inspired by European club football competitions, where organiser generally imposes an association constraint in first round phase: teams from same country cannot be drawn against each other. Its effects are explored both theoretical and simulation models. An round(s) found to increase li...

In this paper we present a new selection algorithm, PICK, and derive by an analysis of its efficiency the (surprising) result that the cost of selection is at most a linear function of the number of input items. In addition, we prove a new lower bound for the cost of selection. The selection problem is perhaps best exemplified by the computation of medians. In general, we may wish to select the...

We find bounds for the domination number of a tournament and investigate the sharpness of these bounds. We also find the domination number of a random tournament.

We classify those triples (n, l,w) for which there exists a ‘knockout’ tournament for n players in which the winner always wins exactly w games and each loser loses exactly l games.