This article begins with a review of previously proposed integer formulations for the maximum diversity problem (MDP). This problem consists of selecting a subset of elements from a larger set in such a way that the sum of the distances between the chosen elements is maximized. We propose a branch and bound algorithm and develop several upper bounds on the objective function values of partial s...

We provide a survey of the major results obtained within the CYBERSAR project in the area of massive data visualization. Despite the impressive improvements in graphics and computational hardware performance, interactive visualization of massive models still remains a challenging problem. To address this problem, we developed methods that exploit the programmability of latest generation graphic...

The cutwidth minimization problem consists of finding a linear layout of a graph so that the maximum linear cut of edges (i.e., the number of edges that cut a line between consecutive vertices) is minimized. This paper starts by reviewing previous exact approaches for special classes of graphs as well as a linear integer formulation for the general problem. We propose a branch and bound algorit...

The article is devoted to the problems of development small and medium-sized businesses in current conditions sanctions

Given two graphs Gi = (Vi, Ei) and G2 = (V2, £2), |Vi| = \V2\ = n, to determine whether they have a size-A; common subgraph is one of the earliest examples of an NP-complete problem (by a trivial reduction from the Maximum Clique problem). We show that this problem for equally sized G\ and G2, i.e. when |23i| = |2?2| = m, remains NP-complete. Moreover, the restriction to the case k = m—tfn, c> ...

Measures of deviation of a symmetric positive deenite matrix from the identity are derived. They give rise to symmetric rank-one, SR1, type updates. The measures are motivated by considering the volume of the symmetric diierence of the two ellipsoids, which arise from the current and updated quadratic models in quasi-Newton methods. The measure deened by the problem-maximize the determinant sub...

At present, the financing of small and medium-sized enterprises in China’s market economy has caused great concern of the whole society. Small and medium-sized enterprises financing difficulties directly affect our country to complete the “public entrepreneurship, people’s innovation” goal. There are many reasons for the financing difficulties of SMEs, such as the small and medium-sized enterpr...

Supply chain management is taken into account as an inseparable component in satisfying customers' requirements. This paper deals with the distribution network design (DND) problem which is a critical issue in achieving supply chain accomplishments. A capable DND can guarantee the success of the entire network performance. However, there are many factors that can cause fluctuations in input dat...

This paper addresses the problem of tracking the covariance matrix eigenstructure, based on SVD (Singular Value Decomposition) updating, of a time-varying data matrix formed from received vectors. This problem occurs frequently in signal processing applications such as adaptive beamforming, direction nding, spectral estimation, etc. As this problem needs to be solved in real time, it is natural...