We define the first nontrivial polynomially recognizable subclass of P-matrixGeneralized Linear Complementarity Problems (GLCPs) with a subexponential pivot rule. No such classes/rules were previously known. We show that a subclass of Shapley turn-based stochastic games, subsuming Condon’s simple stochastic games, is reducible to the new class of GLCPs. Based on this we suggest the new strongly...

Abstract The question whether the Simplex Algorithm admits an efficient pivot rule remains one of most important open questions in discrete optimization. While many natural, deterministic rules are known to yield exponential running times, random-facet was shown have a subexponential time. For long time, Zadeh’s remained prominent candidate for first with We present lower bound construction tha...

In this paper, we study algorithmic questions concerning products of matrices and their consequences for recognition algorithms polyhedra. The 1-product S1∈Rm1×n1,S2∈Rm2×n2 is a matrix in R(m1+m2)×(n1n2) whose columns are the concatenation each column S1 with S2. k-product generalizes 1-product, by taking as input two S1,S2 together k−1 special rows those matrices, outputting certain compositio...

These lectures on the combinatorics and geometry of 0/1-polytopes are meant as an introduction and invitation. Rather than heading for an extensive survey on 0/1polytopes I present some interesting aspects of these objects; all of them are related to some quite recent work and progress. 0/1-polytopes have a very simple definition and explicit descriptions; we can enumerate and analyze small exa...

In this paper we give an introduction to the connection between complexity theory and the study of randomized algorithms. In particular, we will define and study probabilistic complexity classes, survey the basic results, and show how they relate to the notion of randomized algorithms.

We study the GKM theory for a equivariant stratified space having orbifold structures in tis successive quotients. Then, we introduce notion of an \emph{almost simple polytope}, as well \emph{divisive toric variety} generalizing concept divisive weighted projective space. employ to compute generalized cohomology theories varieties associated almost polytopes and varieties.

in this paper, a combinational optimization algorithm is introduced to obtain the best size and location of static compensator (statcom) in power systems. its main contribution is considering contingency analysis where lines outages may lead to infeasible solutions especially at peak loads and it commonly can be vanished by load-shedding. the objective of the proposed algorithm is firstly to pr...

We report a remarkable success of nested pricing rules over major pivot rules commonly used in practice, such as Dantzig’s original rule as well as the steepest-edge rule and Devex rule.