A single-elimination (SE) tournament is a popular way to select a winner in both sports competitions and in elections. A natural and well-studied question is the tournament fixing problem (TFP): given the set of all pairwise match outcomes, can a tournament organizer rig an SE tournament by adjusting the initial seeding so that their favorite player wins? We prove new sufficient conditions on t...

We study the asymptotic behavior of maximum number directed cycles a given length in tournament: let c(ℓ) be limit ratio ℓ an n-vertex tournament and expected random tournament, when n tends to infinity. It is well-known that c(3)=1 c(4)=4/3. show c(ℓ)=1 if only not divisible by four, which settles conjecture Bartley Day. If we 1+2⋅(2/π)ℓ≤c(ℓ)≤1+(2/π+o(1))ℓ determine value exactly for ℓ=8. also...

Abstract Simulating and predicting tournament outcomes has become an increasingly popular research topic. The can be influenced by several factors, such as attack, defence home advantage strength values, well structures. However, the claim that different structures, knockout (KO), round-robin (RR) hybrid have their own time restraints requirements limited evaluation of best structure for a part...

Abstract The FIFA Women’s World Cup tournament consists of a group stage and knockout stage. We identify several issues that create competitive imbalance in the use match data from all tournaments 1991 through 2019 to empirically assess across groups each Cup. Using least squares, we determine ratings for teams. For team, average opponents calculate rating. find range rating varies between 2.5 ...

Competitive fitness is the assessment of an individual’s fitness in the context of competition with other individuals in the evolutionary system. This commonly takes one of two forms: one-population competitive fitness, where competition is solely between individuals in the same population; and N-population competitive fitness, often termed competitive coevolution. In this paper we discuss comm...

Competitive fitness is the assessment of an individual’s fitness in the context of competition with other individuals in the evolutionary system. This commonly takes one of two forms: one-population competitive fitness, where competition is solely between individuals in the same population; and N-population competitive fitness, often termed competitive coevolution. In this paper we discuss comm...

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model of its opponent's strategy based on its past behavior, and uses the model to predict its future behavior. We represent an interaction between agents by a repeated-game and restrict our attention to opponent strategies that can be represented by DFA. Learning a minimal DFA without a teacher was proved to be hard. We presented an unsu-pervised algorithm, US-L , based on Angluin's L algorith...

This paper provides an analysis of a natural k-round tournament over n = 2' players, and demonstrates that the tournament possesses a surprisingly strong ranking property. The ranking property of this tournament is exploited by using it as a building block for efficient parallel sorting algorithms under a variety of different models of computation. Three important applications are provided. Fir...

For a random tournament on 3n vertices, the expected number of Hamiltonian cycles is known to be (3n− 1)!/23 . Let T1 denote a tournament of three vertices v1,v2,v3. Let the orientation be such that there are directed edges from v1to v2 , from v2 to v3 and from v3 to v1. Construct a tournament Ti by making three copies of Ti−1, T ′ i−1, T ′′ i−1 and T ′′′ i−1. Let each vertex in T ′ i−1 have di...