We consider the problem of using simulation to efficiently estimate the win probabilities for participants in a general random knockout tournament. Both of our proposed estimators, one based on the notion of “observed survivals” and the other based on conditional expectation and post-stratification, are highly effective in terms of variance reduction when compared to the raw simulation estimato...

Balanced knockout tournaments are one of the most common formats for sports competitions, and are also used in elections and decision-making. We consider the computational problem of finding the optimal draw for a particular player in such a tournament. The problem has generated considerable research within AI in recent years. We prove that checking whether there exists a draw in which a player...

Preferential attachment networks are a type of random network where new nodes connected to existing ones at random, and more likely connect those that already have many connections. We investigate further family models introduced by Antunovi\'{c}, Mossel R\'{a}cz each vertex in preferential graph is assigned type, based on the types its neighbours. Instances this process proportions present do ...

The elimination or knockout format is one of the most common designs for pairing competitors in tournaments and leagues. In each round of a knockout tournament, the losers are eliminated while the winners advance to the next round. Typically, the goal of such a design is to identify the overall best player. Using a common probability model for expressing relative player strengths, we develop an...

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...

Abstract Negative dependence of sequences random variables is often an interesting characteristic their distribution, as well a useful tool for studying various asymptotic results, including central limit theorems, Poisson approximations, the rate increase maximum, and more. In study probability models tournaments, negative participants’ outcomes arises naturally, with application to results. p...