We present two new perfect hashing schemes that can be used for efficient bitboard move generation for sliding pieces in chess-like board games without the need to use rotated bitboards. Moreover, we show that simple variations of these schemes give minimal perfect hashing schemes. The new method is applicable provided N , the number of k-bit spaced positions that may be set to 1, is not more t...

We model greenhouse gas (GHG) emissions as a dynamic game. Countries’ emissions increase atmospheric concentrations of GHG, which negatively affects all countries' welfare. We analyze self-enforcing climate-change treaties that are supportable as subgame perfect equilibria. A simulation model illustrates conditions where a subgame perfect equilibrium supports the first-best outcome. In one of o...

In the Bose-Einstein condensation of interacting atoms or molecules such as Rb, Na and Li, the theoretical understanding of the transition temperature is not always obvious due to the interactions or zero point energy which cannot be exactly taken into account. The S-wave collision model fails sometimes to account for the condensation temperatures. In this work, we look at the problem within th...

This paper gives a theoretical and empirical analysis of the time complexity of genetic algorithms (GAs) on problems with exponentially scaled building blocks. It is important to study GA performance on this type of problems because one of the difficulties that GAs are generally faced with is due to the low scaling or low salience of some building blocks. The paper is an extension of the model ...

An (s; n; q; t)-perfect hash family is a set of functions 1 ; 2 ; : : :; s from a set V of cardinality n to a set F of cardinality q with the property that every t-subset of V is injectively mapped into F by at least one of the functions i. The paper shows that the maximum value n s;t (q) that n can take for xed s and t has a leading term that is linear in q if and only if t > s. Moreover, for ...

Structural changes in the European natural gas market such as liberalization, increasing domestic demand, and increasing import dependency have triggered new attempts to model these markets accurately. In this paper, we propose an exhaustive model of the European natural gas supply including the possibility of strategic behaviour of the agents along the value-added chain. We structure it as a t...

Certain subgraphs of a given graph G restrict the minimum number χ(G) of colors that can be assigned to the vertices of G such that the endpoints of all edges receive distinct colors. Some of such subgraphs are related to the celebrated Strong Perfect Graph Theorem, as it implies that every graph G contains a clique of size χ(G), or an odd hole or an odd anti-hole as an induced subgraph. In thi...

We present a simple and e cient dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738 761, 1994). The space usage is similar to that of binary search trees, i.e., three words per key on average. The practicality of th...