Computation of arc length in the presence of barriers in networks

Abstract

In the presence of barriers between the pair of nodes, the rectilinear metric in a single step or multiple steps with p = 1 or the Euclidean metric in multiple steps with p = 2 equation L P = [( x i − x j ) p + ( y i − y j ) p ] 1/ p is used to compute the minimum arc length. As a result, the travel path may be a stair case pattern or zigzag pattern and the practical difficulties arise in laying and maintaining the cable. Hence, there is a need to develop a methodology in order to compute the arc length in a single step between the pairs of nodes for which ‘ p’ value is between 1 and 2. This paper presents a mathematical model developed to compute the ‘ p’ values of the curves. The resultant ‘ p’ value is used to compute the arc length ( L P ) of the curves in the presence of barriers for the problem under consideration.