LED deployment optimization in VLC network based on simplicial complexes

2021 ◽  
pp. 1-1
Author(s):  
Zhenghao Li ◽  
Jiangtao Li ◽  
Xu Bao ◽  
Jing Xia
10.37236/1245 ◽  
1996 ◽  
Vol 3 (1) ◽  
Author(s):  
Art M. Duval

Björner and Wachs generalized the definition of shellability by dropping the assumption of purity; they also introduced the $h$-triangle, a doubly-indexed generalization of the $h$-vector which is combinatorially significant for nonpure shellable complexes. Stanley subsequently defined a nonpure simplicial complex to be sequentially Cohen-Macaulay if it satisfies algebraic conditions that generalize the Cohen-Macaulay conditions for pure complexes, so that a nonpure shellable complex is sequentially Cohen-Macaulay. We show that algebraic shifting preserves the $h$-triangle of a simplicial complex $K$ if and only if $K$ is sequentially Cohen-Macaulay. This generalizes a result of Kalai's for the pure case. Immediate consequences include that nonpure shellable complexes and sequentially Cohen-Macaulay complexes have the same set of possible $h$-triangles.


2010 ◽  
Vol 36 (2) ◽  
pp. 242-248 ◽  
Author(s):  
Jie CHEN ◽  
Chen CHEN ◽  
Juan ZHANG ◽  
Bin XIN

2014 ◽  
Vol 31 (2) ◽  
pp. 145
Author(s):  
Yaobin He ◽  
Dian Zhang ◽  
Li Qi ◽  
Shengzhong Feng ◽  
Zhong Ming ◽  
...  

2021 ◽  
Vol 31 (4) ◽  
pp. 041102
Author(s):  
Y. Lee ◽  
J. Lee ◽  
S. M. Oh ◽  
D. Lee ◽  
B. Kahng
Keyword(s):  

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1368 ◽  
Author(s):  
Luoheng Yan ◽  
Yuyao He ◽  
Zhongmin Huangfu

The underwater wireless sensor networks (UWSNs) have been applied in lots of fields such as environment monitoring, military surveillance, data collection, etc. Deployment of sensor nodes in 3D UWSNs is a crucial issue, however, it is a challenging problem due to the complex underwater environment. This paper proposes a growth ring style uneven node depth-adjustment self-deployment optimization algorithm (GRSUNDSOA) to improve the coverage and reliability of UWSNs, meanwhile, and to solve the problem of energy holes. In detail, a growth ring style-based scheme is proposed for constructing the connective tree structure of sensor nodes and a global optimal depth-adjustment algorithm with the goal of comprehensive optimization of both maximizing coverage utilization and energy balance is proposed. Initially, the nodes are scattered to the water surface to form a connected network on this 2D plane. Then, starting from sink node, a growth ring style increment strategy is presented to organize the common nodes as tree structures and each root of subtree is determined. Meanwhile, with the goal of global maximizing coverage utilization and energy balance, all nodes depths are computed iteratively. Finally, all the nodes dive to the computed position once and a 3D underwater connected network with non-uniform distribution and balanced energy is constructed. A series of simulation experiments are performed. The simulation results show that the coverage and reliability of UWSN are improved greatly under the condition of full connectivity and energy balance, and the issue of energy hole can be avoided effectively. Therefore, GRSUNDSOA can prolong the lifetime of UWSN significantly.


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