scholarly journals Bounds on the Size of the Minimum Dominating Sets of Some Cylindrical Grid Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Mrinal Nandi ◽  
Subrata Parui ◽  
Avishek Adhikari
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Domination Number ◽  
Cartesian Product ◽  
Wireless Sensor ◽  
Dominating Sets ◽  
Grid Graph ◽  
Grid Graphs ◽  
Cylindrical Grid ◽  
Domination Numbers

Let γPm □ Cn denote the domination number of the cylindrical grid graph formed by the Cartesian product of the graphs Pm, the path of length m, m≥2, and the graph Cn, the cycle of length n, n≥3. In this paper we propose methods to find the domination numbers of graphs of the form Pm □ Cn with n≥3 and m=5 and propose tight bounds on domination numbers of the graphs P6 □ Cn, n≥3. Moreover, we provide rough bounds on domination numbers of the graphs Pm □ Cn, n≥3 and m≥7. We also point out how domination numbers and minimum dominating sets are useful for wireless sensor networks.

scholarly journals CONE: A Connected Dominating Set-Based Flooding Protocol for Wireless Sensor Networks

Sensors ◽  
2019 ◽  
Vol 19 (10) ◽  
pp. 2378 ◽  
Author(s):  
Dennis Lisiecki ◽  
Peilin Zhang ◽  
Oliver Theel
Keyword(s):  
Energy Efficiency ◽  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Dominating Set ◽  
Average Energy ◽  
Connected Dominating Set ◽  
Wireless Sensor ◽  
Dominating Sets ◽  
Power Sources ◽  
Network Flooding

Wireless sensor networks (WSNs) play a significant role in a large number of applications, e.g., healthcare and industry. A WSN typically consists of a large number of sensor nodes which rely on limited power sources in many applications. Therefore, improving the energy efficiency of WSNs becomes a crucial topic in the research community. As a fundamental service in WSNs, network flooding offers the advantages that information can be distributed fast and reliably throughout an entire network. However, network flooding suffers from low energy efficiency due to the large number of redundant transmissions in the network. In this work, we exploit connected dominating sets (CDS) to enhance the energy efficiency of network flooding by reducing the number of transmissions. For this purpose, we propose a connected dominating set-based flooding protocol (CONE). CONE inhibits nodes that are not in the CDS from rebroadcasting packets during the flooding process. Furthermore, we evaluate the performance of CONE in both simulations and a real-world testbed, and then we compare CONE to a baseline protocol. Experimental results show that CONE improves the end-to-end reliability and reduces the duty cycle of network flooding in the simulations. Additionally, CONE reduces the average energy consumption in the FlockLab testbed by 15%.

scholarly journals Computing the Domination Number of Grid Graphs

10.37236/628 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Samu Alanko ◽  
Simon Crevals ◽  
Anton Isopoussu ◽  
Patric Östergård ◽  
Ville Pettersson
Keyword(s):  
Dynamic Programming ◽  
Dominating Set ◽  
Domination Number ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Dominating Sets ◽  
Grid Graph ◽  
Grid Graphs ◽  
Square Grid ◽  
Minimum Dominating Set

Let $\gamma_{m,n}$ denote the size of a minimum dominating set in the $m \times n$ grid graph. For the square grid graph, exact values for $\gamma_{n,n}$ have earlier been published for $n \leq 19$. By using a dynamic programming algorithm, the values of $\gamma_{m,n}$ for $m,n \leq 29$ are here obtained. Minimum dominating sets for square grid graphs up to size $29 \times 29$ are depicted.

Wireless Sensor Networks Management Using Differential Evolution and Minimum Dominating Sets

2021 ◽  
Author(s):  
Abdel-Rahman Hedar ◽  
Ayman Ayad ◽  
Moumen T. El-Melegy ◽  
Usama Sayed ◽  
Gamal A. El-Sayed
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Differential Evolution ◽  
Wireless Sensor ◽  
Dominating Sets
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