In this note, the cut C is referred as the cut-set and the size of the cut |C| as the size of the cut-set. For a graph, a maximum cut is a cut whose size is at least the size of any other cut. The problem of finding a maximum cut in a graph is known as the maximum cut problem. The problem is NP-hard. Simple 0.5approximation algorithms existed long time ago, but no improvement was made till 1990...

In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes. 

Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new algorithm for computing the detour index of molecular graphs is presented. We apply our algorithm on copper and silver nanoclusters ...

A new algorithm for classification of DMUs to efficient and inefficient units in data envelopment analysis is presented. This algorithm uses the non-Archimedean Charnes-Cooper-Rhodes[1] (CCR) model. Also, it applies an assurance value for the non-Archimedean                          using only simple computations on inputs and outputs of DMUs (see [18]). The convergence and efficiency of the ne...