Knuth and Moore presented a theoretical lower bound on the number of leaves that any fixed-depth minimax tree-search algorithm traversing a uniform tree must explore, the so-called minimal tree. Since real-life minimax trees aren’t uniform, the exact size of this tree isn’t known for most applications. Further, most games have transpositions, implying that there exists a minimal graph which is ...

For irregular architectures global register allocation remains a challenging problem, and has received a lot of attention in recent years. The classical graph-colouring analogy used by Chaitin and Briggs is not adequate for irregular architectures featuring non-orthogonal instruction sets and irregular register sets. Previous work [1, 2] on register allocation based on partitioned boolean quadr...

We present a new explicit construction for expander graphs with nearly optimal spectral gap. The construction is based on a series of 2-lift operations. Let G be a graph on n vertices. A 2-lift of G is a graph H on 2n vertices, with a covering map π :H →G. It is not hard to see that all eigenvalues of G are also eigenvalues of H . In addition, H has n “new” eigenvalues. We conjecture that every...

We consider nonlinear stochastic programming problems with probabilistic constraints. The concept of a p-efficient point of a probability distribution is used to derive equivalent problem formulations, and necessary and sufficient optimality conditions. We analyze the dual functional and its subdifferential. Two numerical methods are developed based on approximations of the p-efficient frontier...

the system analysis plays an important role in natural resources, water resources and industrial engineering. in recent years, most parts of iran like golestan province, due to the lack of integrated river basin management, have been suffered numerous losses in variant environmental, social and economic aspects. in this paper an application of system analysis has been applied to optimal pattern...

the aim of this study was to develop an optimal sustainable forest plantation based on goal programming and analytic hierarchy process (ahp) methods. this study was carried out in guilan province, north of iran. first of all, the ecological capability of the study area for plantation establishment/maintenance was evaluated based on multi-factor method and specific ecological makhdoum model by m...

in this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear programming (abbreviated to fflp) problems. also, we employ linear programming (lp) with equality constraints to find a nonegative fuzzy number vector x which satisfies ax =b, where a is a fuzzy number matrix. then we investigate the existence of a positive solution of fully fuzzy linear system (ffls).