We study lines through the origin of finite-dimensional complex vector spaces that enjoy a doubly transitive automorphism group. In doing so, we make fundamental connections with both discrete geometry and algebraic combinatorics. particular, show are necessarily optimal packings in projective space, introduce fruitful generalization regular abelian distance-regular antipodal covers complete gr...

We survey some recent results on long-standing conjectures regarding Hamilton cycles in directed graphs, oriented graphs and tournaments. We also combine some of these to prove the following approximate result towards Kelly’s conjecture on Hamilton decompositions of regular tournaments: the edges of every regular tournament can be covered by a set of Hamilton cycles which are ‘almost’ edge-disj...

Sorting of transitive total ordered sets is one of the best investigated topics in Computer Science. A generalization of this is sorting an intransitive total ordered set which is more complex. While a transitive total ordered set (e. g. a subset of the real numbers) holds a ≥ b∧b ≥ a⇒ a ≥ c, this does not have to be true for a intransitive total ordered set. Only a → b ∨̇ b → a is claimed. Neve...

The NCAA selects teams for their championship tournaments using a selection committee. For the Men’s Division I NCAA Basketball Tournament the committee must factor in the results of over 5,000 regular season games, as well as other qualitative factors. One of the key summary statistics used by the committee during the process is the Rating Percentage Index (RPI). This paper evaluates the commi...

We prove that every Eulerian orientation of Km,n contains 1 4+ √ 8 mn(1 − o(1)) arc-disjoint directed 4-cycles, improving earlier lower bounds. Combined with a probabilistic argument, this result is used to prove that every regular tournament with n vertices contains 1 8+ √ 32 n2(1−o(1)) arc-disjoint directed 4-cycles. The result is also used to provide an upper bound for the distance between t...

In [8] a new data structure called semi-heap is proposed to construct an optimal (n logn) sorting algorithm to sort an intransitive total ordered set, a generalization of regular sorting. In this part, we provide a cost-optimal parallel algorithm using semi-heap. The run time of this algorithm is (n) with (logn) processors under the EREW PRAM model. The use of a Hamiltonian path (generalized so...

This paper presents the first performance results for Ballard’s *-Minimax algorithms applied to a real–world domain: backgammon. It is shown that with effective move ordering and probing the Star2 algorithm considerably outperforms Expectimax. Star2 allows strong backgammon programs to conduct depth 5 full-width searches (up from 3) under tournament conditions on regular hardware without using ...

In the team described in this paper we realize a direct approach to soccer agents for the simulation league of the RoboCup '98-tournament. Its backbone is formed by a detailed world model. Based on information which is reconstructed on the world model level, the rule-based decision levels chose a relevant action. The architecture for the goalie is diierent from the regular players, introducing ...

In the team described in this paper we realize a direct approach to soccer agents for the simulation league of the RoboCup '98-tournament. Its backbone is formed by a detailed world model. Based on information which is reconstructed on the world model level, the rule-based decision levels chose a relevant action. The architecture for the goalie is diierent from the regular players, introducing ...