Making a tournament k $k$‐strong

The number of pancyclic arcs in a k-strong tournament

A tournament is a digraph, where there is precisely one arc between every pair of distinct vertices. An arc is pancyclic in a digraph D, if it belongs to a cycle of length l, for all 3 <= l <= |V (D)|. Let p(D) denote the number of pancyclic arcs in a digraph D and let h(D) denote the maximum number of pancyclic arcs belonging to the same Hamilton cycle of D. Note that p(D) >= h(D). Moon showed...

Efficient Simulation of a Random Knockout Tournament

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...

Pixel Consistency, K-Tournament Selection, and Darwinian-Based Feature Extraction

In this paper, we present a two-stage process for developing feature extractors (FEs) for facial recognition. In this process, a genetic algorithm is used to evolve a number of local binary patterns (LBP) based FEs with each FE consisting of a number of (possibly) overlapping patches from which features are extracted from an image. These FEs are then overlaid to form what is referred to as a hy...

Tournament Solutions and Their Applications to Multiagent Decision Making

A Prediction Tournament Paradox

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 forecasters will likely score better. This is true for one-on-one comparisons between contestants. But consider a realistic-size tournament with many contestants...