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\section{Literature Review}\label{sec:lit_review}
\section*{Literature Review}\label{sec:lit_review}
The Minimum Spanning Tree (MST) is a potential routing protocol for mesh-based Wireless Sensor Networks (WSN). Algorithms like Prim's \cite{cormen_introduction_2009} and Kruskal's \cite{kruskal_shortest_1956} have attacted implementations in applications since they are simple to implement and effective in static networks, However, their direct application to Wireless Sensor Networks (WSNs) remains questionable.
% The Minimum Spanning Tree (MST) algorithms, exemplified by Prim's \cite{cormen_introduction_2009} and Kruskal's \cite{kruskal_shortest_1956}, have gained renown for their simplicity and effectiveness in structuring static mesh networks. However, their direct application in Wireless Sensor Networks (WSNs) necessitates further investigation.
Recent research endeavors have delved into the potential of MSTs to enhance energy efficiency within WSN routing protocols. For instance, MSTEAM leverages localized MSTs to facilitate multicast routing, thereby minimizing energy consumption during message propagation \cite{frey_localized_2007}. Similarly, NNT offers a distributed approach to construct approximate MSTs, effectively reducing communication overhead \cite{4492767}. Additionally, CMSTR addresses the challenge of imbalanced energy consumption in hierarchical routing by employing constrained MSTs to establish energy-efficient intra-cluster communication paths \cite{lin_cmstr_2023}. These advancements highlight the promise of MST-based strategies in promoting energy-aware routing within WSNs, especially in $CO_2$ monitoring applications and specific deployment scenarios.
Recent research endeavors have delved into the potential of MSTs to enhance energy efficiency within WSN routing protocols. For instance, MSTEAM leverages localized MSTs to facilitate multicast routing, thereby minimizing energy consumption during message propagation \cite{frey_localized_2007}. Similarly, NNT offers a distributed approach to construct approximate MSTs, effectively reducing communication overhead \cite{4492767}. Additionally, CMSTR addresses the challenge of imbalanced energy consumption in hierarchical routing by employing constrained MSTs to establish energy-efficient intra-cluster communication paths \cite{lin_cmstr_2023}. These advancements highlight the promise of MST-based strategies in promoting energy-aware routing within WSNs, especially in CO2 monitoring applications and specific deployment scenarios.
In an MST-based WSN, there is necessity for each node to compute shortest paths to all others, which significantly escalates complexity and energy consumption \cite{wan_minimum-energy_2001}. Moreover, the static nature of MSTs requires recalculations upon network alterations, potentially causing delays and packet loss. In complex environments, MSTs may not always ensure the most energy-efficient paths, further complicating their practical utility.
There is necessity for each node to compute shortest paths to all others significantly escalates complexity and energy consumption. Moreover, the static nature of MSTs requires recalculations upon network alterations, potentially causing delays and packet loss. In complex environments, MSTs may not always ensure the most energy-efficient paths, further complicating their practical utility.
Nevertheless, MSTs offer inherent advantages such as simplicity, scalability, and fault tolerance, making them worth exploring. A potential solution could adopt a reactive approach, where the sink node initiates data collection through controlled broadcasts or multicasts. Subsequently, leaf nodes transmit data along pre-computed, energy-efficient paths towards the sink, facilitated by intermediate nodes. This reactive paradigm appears promising for static WSN deployments, providing a balance between simplicity and efficiency.
In conclusion, while MSTs exhibit limitations in certain WSN scenarios, their adaptability and potential for energy-efficient routing make them a compelling area for further investigation, particularly in CO2 monitoring applications. Future research should focus on refining MST-based strategies to address the dynamic nature of WSNs and optimize energy consumption under varying deployment conditions.
% In the case of WSNs, there must be an optimal tree building algorithm for routing packets of data from point to point in a mesh network. Since the introduction of the abovementioned algorithms, there has since been an evolution of those ideas built for low powered networks like WSNs, they include MSTEAM \cite{frey_localized_2007}, NNT \cite{4492767} and CSMTR \cite{lin_cmstr_2023}.
% These algorithms were devleoped for one purpose ---to reduce the energy required during building of the graph at each node when there is a change in the topology (new node joins or node dies).
% Traditionally, MSTs connect to all nodes, akin to a mesh topology, this would allow nodes to calculate the weights from each vertice connected to itself and thereby calculating the shortest or optimal path from node to node.
% A key pitfall is the static nature of MSTs. A change in the network would require recalculations, leading to potential delay and packet loss, thereby affecting the efficiency of the data transmission. Additionally, MSTs may not always provide the most optimal path, especially in complex environments.
% A potential proof of concept of this algorithm could feature a reactive system, where the sink node would initiate a request for data collection either through broadcast or multicast via their nearest neighbour. Each leaf node would then unicast their data packets through an optimal path that would have been pre-calculated, and the data will then be forwarded through the optimal paths of the subsequent nodes. In a WSN where nodes would be deployed in a static environment, this solution would a viable choice.
% Monitoring environmental conditions like air quality or wildfire risk is crucial, and Wireless Sensor Networks (WSNs) offer a promising solution. But designing efficient and reliable WSNs presents challenges, particularly in balancing low-power consumption with robust data transmission a key concern in the realm of Internet of Things (IoT) \cite{hemanand_enabling_2021}.
% Star-based Wireless Sensor Networks (WSNs) have emerged as a popular approach for environmental monitoring, exemplified by Lazarescu et al.'s wildfire detection system \cite{lazarescu_design_2013}. These networks resemble constellations, with individual sensor nodes dispersed like stars and transmitting data to a central gateway node, analogous to a central star. This architecture prioritizes reliable communication, particularly crucial in scenarios like wildfire detection, by utilizing dedicated radio channels within the unlicensed Industrial, Scientific, and Medical (ISM) band \cite{shah_iot-enabled_2020}. The central gateway node acts as a hub, collecting and buffering data from all sensors before forwarding it to a remote server via the internet.
% Building upon this concept, Shah et al. crafted a similar system, but with sensors directly tethered to a computer through a dedicated transceiver pair \cite{shah_iot-enabled_2020}. This setup streamlines data visualization and sharing, but lacks the centralized structure of its predecessor. Interestingly, star topologies have even ventured into the realm of long-range communication, utilizing technologies like 2G/GSM to shine their light over wider areas \cite{CVZZ16}.
% While Star-based WSNs shine in terms of simplicity and ease of deployment, they face limitations. Scaling them up for wider coverage can be challenging \cite{Boukerche2018Connectivity}. Additionally, research by Shrestha et al. suggests that Mesh networks, with their interconnected nodes and redundant data paths, may offer superior reliability, especially when individual nodes fail \cite{shrestha_performance_2007}.
% Therefore, choosing the right WSN topology for environmental monitoring requires careful consideration. Simplicity and ease of deployment offered by Star networks might be ideal for smaller, controlled environments \cite{Alippi2011A}. However, for expansive or critical monitoring applications, the enhanced reliability of Mesh networks may be the brighter star to follow \cite{Han2011Reliable}.
Nevertheless, MSTs offer a hierarchical routing topology, which has been proven to be scalable and energy efficient in WSNs \cite{liu_atypical_2015}. A potential solution could adopt a reactive approach, where the sink node initiates data collection through controlled broadcasts or multicasts. Subsequently, leaf nodes transmit data along pre-computed, energy-efficient paths towards the sink, facilitated by intermediate nodes. This reactive paradigm appears promising for static WSN deployments, providing a balance between simplicity and efficiency.
In conclusion, while MSTs exhibit limitations in certain WSN scenarios, their adaptability and potential for energy-efficient routing make them a compelling area for further investigation, particularly in $CO_{2}$ monitoring applications.
\newpage
\printbibliography
\end{document}

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date = {1956},
note = {Publisher: American Mathematical Society},
}
@inproceedings{wan_minimum-energy_2001,
title = {Minimum-energy broadcast routing in static ad hoc wireless networks},
volume = {2},
url = {https://ieeexplore.ieee.org/document/916310},
doi = {10.1109/INFCOM.2001.916310},
abstract = {Energy conservation is a critical issue in ad hoc wireless networks for node and network life, as the nodes are powered by batteries only. One major approach for energy conservation is to route a communication session along the routes which requires the lowest total energy consumption. This optimization problem is referred to as minimum-energy routing. While minimum-energy unicast routing can be solved in polynomial time by shortest-path algorithms, it remains open whether minimum-energy broadcast routing can be solved in polynomial time, despite the {NP}-hardness of its general graph version. Previously three greedy heuristics were proposed in Wieselthier et al. (2000): {MST} (minimum spanning tree), {SPT} (shortest-path tree), and {BIP} (broadcasting incremental power). They have been evaluated through simulations in Wieselthier et al.], but little is known about their analytical performance. The main contribution of this paper is the quantitative characterization of their performances in terms of approximation ratios. By exploring geometric structures of Euclidean {MSTs}, we have been able to prove that the approximation ratio of {MST} is between 6 and 12, and the approximation ratio of {BIP} is between /sup 13///sub 3/ and 12. On the other hand, the approximation ratio of {SPT} is shown to be at least /sup n///sub 2/, where n is the number of receiving nodes. To our best knowledge, these are the first analytical results for minimum-energy broadcasting.},
eventtitle = {Proceedings {IEEE} {INFOCOM} 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the {IEEE} Computer and Communications Society (Cat. No.01CH37213)},
pages = {1162--1171 vol.2},
booktitle = {Proceedings {IEEE} {INFOCOM} 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the {IEEE} Computer and Communications Society (Cat. No.01CH37213)},
author = {Wan, P.-J. and Calinescu, G. and Li, X.-Y. and Frieder, O.},
urldate = {2024-02-10},
date = {2001-04},
note = {{ISSN}: 0743-166X},
keywords = {Analytical models, Batteries, Broadcasting, Energy conservation, Energy consumption, Polynomials, Routing, Tree graphs, Unicast, Wireless networks},
file = {IEEE Xplore Abstract Record:/home/junwei/Zotero/storage/5B9MZ4FJ/916310.html:text/html;Submitted Version:/home/junwei/Zotero/storage/T5NITGCK/Wan et al. - 2001 - Minimum-energy broadcast routing in static ad hoc .pdf:application/pdf},
}
@article{liu_atypical_2015,
title = {Atypical Hierarchical Routing Protocols for Wireless Sensor Networks: A Review},
volume = {15},
issn = {1558-1748},
url = {https://ieeexplore.ieee.org/document/7124398},
doi = {10.1109/JSEN.2015.2445796},
shorttitle = {Atypical Hierarchical Routing Protocols for Wireless Sensor Networks},
abstract = {Hierarchical routing in wireless sensor networks ({WSNs}) is a very important topic that has been attracting the research community in the last decade. Typical hierarchical routing is called clustering routing, in which the network is divided into multiple clusters. Recently, some types of atypical hierarchical routing arise, including chain-based, tree-based, grid-based routing, and area-based routing. There are several survey papers that present and compare the hierarchical routing protocols from various perspectives, but a survey on atypical hierarchical routing is still missing. This paper makes a first attempt to provide a comprehensive review on atypical hierarchical routing. We offer a classification of atypical hierarchical routing of {WSNs}, and give detailed analysis of different logical topologies. The most representative atypical hierarchical routing protocols are described, discussed, and qualitatively compared. In particular, the advantages and disadvantages of different atypical hierarchical routing protocols are analyzed with respect to their significant performances and application scenarios. Finally, we put forward some open issues concerning the design of hierarchical {WSNs}. This survey aims to provide useful guidance for system designers on how to evaluate and select appropriate logical topologies and hierarchical routing protocols for specific applications.},
pages = {5372--5383},
number = {10},
journaltitle = {{IEEE} Sensors Journal},
author = {Liu, Xuxun},
urldate = {2024-02-10},
date = {2015-10},
note = {Conference Name: {IEEE} Sensors Journal},
keywords = {area-based, atypical hierarchical routing, chain-based, Data communication, Energy consumption, grid-based, Routing, Routing protocols, Sensors, Topology, tree-based, Wireless sensor networks},
file = {IEEE Xplore Abstract Record:/home/junwei/Zotero/storage/K9II5R3A/7124398.html:text/html;IEEE Xplore Full Text PDF:/home/junwei/Zotero/storage/EEEQLHTQ/Liu - 2015 - Atypical Hierarchical Routing Protocols for Wirele.pdf:application/pdf},
}