The sequence counting the number of unique tournaments with n people is the same as the sequence counting non-tracking binary strings corresponding to n − 2 radar observations with the tracking rule “3 out of 5 with loss 2.” This fact allows us to build a bijection between unique tournaments and non-tracking binary strings.

In this paper we give ratio 4 deterministic and randomized approximation algorithms for the FEEDBACK ARC SET problem in bipartite tournaments. We also generalize these results to give a factor 4 deterministic approximation algorithm for FEEDBACK ARC SET problem in multipartite tournaments. © 2007 Elsevier B.V. All rights reserved.

We characterize weakly Hamiltonian-connected ordinary multipartite tournaments. Our result generalizes such a characterization for tournaments by Thomassen and implies a polynomial algorithm to decide the existence of a Hamiltonian path connecting two given vertices in an ordinary multipartite tournament and find one, if it exists.

A tournament is acyclically indecomposable if no acyclic autonomous set of vertices has more than one element. We identify twelve infinite acyclically indecomposable tournaments and prove that every infinite acyclically indecomposable tournament contains a subtournament isomorphic to one of these tournaments. The profile of a tournament T is the function φT which counts for each integer n the n...

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...

The pattern of a matrix M is a (0, 1)-matrix which replaces all non-zero entries of M with a 1. A directed graph is said to support M if its adjacency matrix is the pattern of M . If M is an orthogonal matrix, then a digraph which supports M must satisfy a condition known as quadrangularity. We look at quadrangularity in tournaments and determine for which orders quadrangular tournaments exist....

In this paper, we begin a classification of the vertex-transitive tournaments of order pq where p and q are distinct odd primes. In particular we characterize the pq-circulant tournaments; see Theorem 4.3. Moreover, we determine 2-closed (in Wielandt’s sense) oddorder transitive permutation groups of degree p and pq by using the classifications of vertextransitive tournaments of order p and pq....

We examine the value added of tournaments that compare the predictive power of behavioral models. The advantages and disadvantages of this particular method have not been systematically discussed in the literature; here we aspire to do so. We conclude that tournaments are a useful addition to our arsenal of methods and a significant step forward in the study of the predictive power of behaviora...

Big data and predictive analytics have the potential to make cities more efficient. Yet cities often lack the resources to use new data and methods effectively, and private researchers often lack the incentives to help solve the problems that cities face. New platforms—such as Kaggle, TopCoder, and DrivenData—now enable governments and other organizations to outsource large-scale prediction pro...

A collection of unlabelled tournaments P is called a hereditary property if it is closed under isomorphism and under taking induced sub-tournaments. The speed of P is the function n 7→ |Pn|, where Pn = {T ∈ P : |V (T )| = n}. In this paper, we prove that there is a jump in the possible speeds of a hereditary property of tournaments, from polynomial to exponential speed. Moreover, we determine t...