No abstract

Given a set of n ≥ 1 unit disk robots in the Euclidean plane, we consider the fundamental problem of providing mutual visibility to them: the robots must reposition themselves to reach a configuration where they all see each other. This problem arises under obstructed visibility, where a robot cannot see another robot if there is a third robot on the straight line segment between them. This problem was solved by Sharma et al. [17] in the luminous robots model, where each robot is equipped with an externally visible light that can assume colors from a fixed set of colors, using 9 colors and O(n) rounds. In this work, we present an algorithm that requires only 3 colors and O(n) rounds.

No abstract

The algorithms of tensors’ summing, multiplying and collapsing are observed in that issue from the perspectives of those paralleling possibilities. The graphs of these algorithms are developed and analyzed from the point of the forecasted values of the acceleration and efficiency. It is assumed that the time of execution for all computing operations is same and equal to a unit of time, and data transfer between computer devices is performed instantaneously without any time consuming (it is acceptable, for example, a parallel computing systems with shared memory). In particular, it is shown that for the tensors’ addition the time of the fastest execution of algorithm for an unlimited number of processors is equal to the length of the maximum path in the graph. In other words, the minimum time of the algorithm will be achieved when the number of processors is equal to the number of components of the tensor. A similar analysis was performed for the algorithms of multiplication and convolution of tensors.