Given a graph ( , ) G N E  , the Covering Salesman Problem (CSP) is to identify the minimum length tour “covering” all the nodes. More specifically, it seeks the minimum length tour visiting a subset of the nodes in N such that each node i not on the tour is within a predetermined distance di of a node on the tour. In this paper, we define and develop a generalized version of the CSP, and refe...

Motivated by an application to database linear querying, such as private information-retrieval protocols, we suggest a fundamental property of codes– the generalized covering radius. The covering-radius hierarchy code characterizes trade-off between storage amount, latency, and access complexity, in systems. Several equivalent definitions are provided, showing this combinatorial, geometric, alg...

In this paper, we study the Generalized Bin Covering problem. For this problem an exact algorithm is introduced which can nd optimal solution for small scale instances. To nd a solution near optimal for large scale instances, a heuristic algorithm has been proposed. By computational experiments, the eciency of the heuristic algorithm is assessed.

The analytical calculation of the area moments inertia used for special mechanical tests in materials science and further generalizations different orders broader symmetry properties has led to a new type trigonometric power sums. corresponding generalized equations are presented, proven, their characteristics discussed. Although sums have basic form, results quite properties, dependent on valu...

Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system...