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Keywords = DCMST

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17 pages, 345 KiB  
Article
Degree-Constrained Minimum Spanning Hierarchies in Graphs
by Miklos Molnar
Algorithms 2024, 17(10), 467; https://doi.org/10.3390/a17100467 - 21 Oct 2024
Cited by 1 | Viewed by 1550
Abstract
The minimum spanning tree problem in graphs under budget-type degree constraints (DCMST) is a well-known NP-hard problem. Spanning trees do not always exist, and the optimum can not be approximated within a constant factor. Recently, solutions have been proposed to solve degree-constrained spanning [...] Read more.
The minimum spanning tree problem in graphs under budget-type degree constraints (DCMST) is a well-known NP-hard problem. Spanning trees do not always exist, and the optimum can not be approximated within a constant factor. Recently, solutions have been proposed to solve degree-constrained spanning problems in the case of limited momentary capacities of the nodes. For a given node, the constraint represents a limited degree of the node for each visit. Finding the solution with minimum cost is NP-hard and the related algorithms are not trivial. This paper focuses on this new spanning problem with heterogeneous capacity-like degree bounds. The minimum cost solution corresponds to a graph-related structure, i.e., a hierarchy. We study the conditions of its existence, and we propose its exact computation, a heuristic algorithm, and its approximation. Full article
(This article belongs to the Special Issue Graph Theory and Algorithmic Applications: Theoretical Developments)
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16 pages, 899 KiB  
Article
An Optimization Routing Algorithm for Green Communication in Underground Mines
by Heng Xu, Qiyue Li, Jianping Wang, Guojun Luo, Chenghui Zhu and Wei Sun
Sensors 2018, 18(6), 1950; https://doi.org/10.3390/s18061950 - 15 Jun 2018
Cited by 7 | Viewed by 3969
Abstract
With the long-term dependence of humans on ore-based energy, underground mines are utilized around the world, and underground mining is often dangerous. Therefore, many underground mines have established networks that manage and acquire information from sensor nodes deployed on miners and in other [...] Read more.
With the long-term dependence of humans on ore-based energy, underground mines are utilized around the world, and underground mining is often dangerous. Therefore, many underground mines have established networks that manage and acquire information from sensor nodes deployed on miners and in other places. Since the power supplies of many mobile sensor nodes are batteries, green communication is an effective approach of reducing the energy consumption of a network and extending its longevity. To reduce the energy consumption of networks, all factors that negatively influence the lifetime should be considered. The degree constraint minimum spanning tree (DCMST) is introduced in this study to consider all the heterogeneous factors and assign weights for the next step of the evaluation. Then, a genetic algorithm (GA) is introduced to cluster sensor nodes in the network and balance energy consumption according to several heterogeneous factors and routing paths from DCMST. Based on a comparison of the simulation results, the optimization routing algorithm proposed in this study for use in green communication in underground mines can effectively reduce the network energy consumption and extend the lifetimes of networks. Full article
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