On Finding Minimum and Maximum Path Length in Grid-Based Wireless Networks

Faiza Al-Salti,Alzeidi N,Khaled Day,Bassel Arafeh

doi:10.5121/ijwmn.2018.10105

Abstract

In this paper, we obtain the minimum and maximum hop counts between any pair of cells in the 3D gridbased wireless networks. We start by determining the minimum path length between any two points in a 2D grid coordinate system. We establish that the minimum path length is the maximum difference between the corresponding coordinates of the two points. We then extend the result to derive the minimum and maximum hop counts for the 3D grid-based wireless networks. We establish that the maximum path length is the sum of the differences between the corresponding coordinates of the two cells. Whilst the minimum path length depends on the positions of the two cells; it does not exceed the maximum difference between the corresponding coordinates of the two cells.

Highlights

The path length or hop count in a wireless network is the number of communication steps needed to send a packet from a source node to a destination node in the network
We have first derived the length of the shortest paths connecting any two points in a 2D grid coordinate system
The obtained result shows that the path length is equal to the maximum difference between the corresponding coordinates of the two points

Summary

INTRODUCTION

The path length or hop count in a wireless network is the number of communication steps needed to send a packet from a source node to a destination node in the network. K. Day et al [6] considered finding a maximum number of node-disjoint paths of minimum or near minimum lengths between any two points of the k-ary n-cube interconnection network. Day et al [6] considered finding a maximum number of node-disjoint paths of minimum or near minimum lengths between any two points of the k-ary n-cube interconnection network These paths are used to derive the fault diameter of the network. We use a similar strategy to derive the minimum and maximum path length between any source-destination pair of cells for the 3D grid-based wireless networks.

DETERMINING PATH LENGTH IN A 2D GRID COORDINATE SYSTEM

OVERVIEW OF THE 3D GRID-BASED WIRELESS NETWORKS

PATH LENGTHS FOR THE 3D GRID STRUCTURE

Case 1: sx = dx & sy = dy & sz > 0

CONCLUSION