Needless to say, sorting, especially sorting by comparisons, has been a classical problem in computer science. Despite its enormous importance, the complexity, in terms of the number of comparisons needed, is simple to analyze. Straightforward information theoretical argument gives the tight lower bound of log2(n!), which is achieved by several simple sorting algorithms, for example, Insertion ...

We prove an a priori lower bound for the pressure, or p-norm joint spectral radius, of a measure on the set of d × d real matrices which parallels a result of J. Bochi for the joint spectral radius. We apply this lower bound to give new proofs of the continuity of the affinity dimension of a selfaffine set and of the continuity of the singular-value pressure for invertible matrices, both of whi...

We compute the pressure of the random energy model (REM) and generalized random energy model (GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra’s “broken replica symmetry bounds”, and identify the random probability cascade as the appropriate random overlap structure for the model. For the REM the lower bound is obtained, in the high temperature...

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of...

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of...

In this paper the eccentric forward extrusion of sections has been simulated and analyzed using FEM Abaqus-explicit. The results have been compared to those obtained from upper bound theorem and experimental works. Close agreements was observed between the FEM and experimental work and as compared with the upper bound data more realistic and better predictions were made by the authors’ method. ...

Given a graph G, a visual cryptography scheme based on the graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper we apply maximal independent sets of the grap...

We show that an improvement to the best known quantum lower bound for Graph-Collision problem implies an improvement to the best known lower bound for Triangle problem in the quantum query complexity model. In Graph-Collision we are given free access to a graph (V,E) and access to a function f : V → {0, 1} as a black box. We are asked to determine if there exist (u, v) ∈ E, such that f(u) = f(v...

A (d − 1)-dimensional simplicial complex is called balanced if its underlying graph admits a proper d-coloring. We show that many well-known face enumeration results have natural balanced analogs (or at least conjectural analogs). Specifically, we prove the balanced analog of the celebrated Lower Bound Theorem for normal pseudomanifolds and characterize the case of equality; we introduce and ch...