Abstract

With both computational complexity and storage space bounded by a small constant, greedy routing is recognized as an appealing approach to support scalable routing in wireless sensor networks. However, significant challenges have been encountered in extending greedy routing from 2D to 3D space. In this research, we develop decentralized solutions to achieve greedy routing in 3D sensor networks. Our proposed approach is based on a unit tetrahedron cell (UTC) mesh structure. We propose a distributed algorithm to realize volumetric harmonic mapping (VHM) of the UTC mesh under spherical boundary condition. It is a one-to-one map that yields virtual coordinates for each node in the network without or with one internal hole. Since a boundary has been mapped to a sphere, node-based greedy routing is always successful thereon. At the same time, we exploit the UTC mesh to develop a face-based greedy routing algorithm and prove its success at internal nodes. To deliver a data packet to its destination, face-based and node-based greedy routing algorithms are employed alternately at internal and boundary UTCs, respectively. For networks with multiple internal holes, a segmentation and tunnel-based routing strategy is proposed on top of VHM to support global end-to-end routing. As far as we know, this is the first work that realizes truly deterministic routing with constant-bounded storage and computation in general 3D wireless sensor networks.

Highlights

  • With both its computational complexity and storage space bounded by a small constant, greedy routing is known for its scalability to large networks with stringent resource constraints on individual nodes

  • Since a boundary has been mapped to a sphere, node-based greedy routing is always successful thereon

  • For networks with multiple internal holes, a segmentation and tunnel-based routing strategy is proposed on top of volumetric harmonic mapping (VHM) to support global end-to-end routing

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Summary

Introduction

With both its computational complexity and storage space bounded by a small constant, greedy routing is known for its scalability to large networks with stringent resource constraints on individual nodes. We propose a distributed algorithm to realize volumetric harmonic mapping of the UTC mesh under a spherical boundary condition It is a one-to-one map that yields virtual coordinates for each node in the network. We exploit the UTC mesh to develop a face-based greedy routing algorithm and prove its success at internal nodes. To route a data packet to its destination, face-based and node-based greedy routing algorithms are employed alternately at internal and boundary UTCs, respectively.

Construction of Unit Tetrahedron Cells
Routing at Internal UTCs
Routing in 3D Sensor Network without Internal Holes
Volumetric Embedding
Volumetric Harmonic Function
Spherical Harmonic Function
Distributed Mapping Algorithm
Distributed Spherical Harmonic Map
Distributed Volumetric Harmonic Map
The Routing Algorithm
Routing in 3D Sensor Network with Internal Holes
Network Segmentation and Mapping
Tunnel Routing
Applications and Simulations
Peer-to-Peer Greedy Routing
Stretch Factor
Load Distribution
Data Storage and Retrieval
Where to Store the Data
Route Data and Query
Networks with Multiple Internal Holes
Performance
Findings
Conclusions
Full Text
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