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Mathematics of OR: Significance and Application of Virtual Directions in Reducing Computational Efficiency in Network Optimization


Santosh Kumar, Elias Munapo, Philimon Nyamugure, Trust Tawanda
Pages: 33-48
ISBN: 978-93-5834-434-9


Emerging Trends in Applied Research (Volume -3)

Emerging Trends in Applied Research
(Volume - 3)

Abstract

Usually, analysis of a directed network with respect to a particular problem is computationally less demanding when compared to a similar situation analysed for the non-directed network. For example, the shortest route problem has applications in directed as well as in non-directed networks. However, computational complexity for finding the shortest path in a directed network is less compared to the same shortest path in a non-directed network. This paper, first reviews the concept of virtual directions, briefly point out an application in context of reliability and presents a simpler version of virtual directions to find the shortest route between two specified nodes in a non-directed network. The convergence is guaranteed in at most (n-1) number of iterations in an ‘n’ node non-directed network. Purpose of the paper is to simplify the concept of virtual directions and appeal other researchers to extend use of the virtual directions in analysis of other network problems in non-directed networks.

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© Integrated Publications.
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