New computational approaches for the power dominating set problem: Set covering and the neighborhoods of zero forcing forts

Networks ◽  
2021 ◽  
Author(s):  
Logan A. Smith ◽  
Illya V. Hicks
Keyword(s):  
Dominating Set ◽  
Set Covering ◽  
Zero Forcing ◽  
Computational Approaches ◽  
Dominating Set Problem

MINIMUM CONNECTED r-HOP k-DOMINATING SET IN WIRELESS NETWORKS

2009 ◽  
Vol 01 (01) ◽  
pp. 45-57 ◽  
Author(s):  
DEYING LI ◽  
LIN LIU ◽  
HUIQIANG YANG
Keyword(s):  
Wireless Networks ◽  
Undirected Graph ◽  
Dominating Set ◽  
Approximation Ratio ◽  
Dominating Set Problem ◽  
Simulation Results

In this paper, we study the connected r-hop k-dominating set problem in wireless networks. We propose two algorithms for the problem. We prove that algorithm I for UDG has (2r + 1)3 approximate ratio for k ≤ (2r + 1)2 and (2r + 1)((2r + 1)2 + 1)-approximate ratio for k > (2r + 1)2. And algorithm II for any undirected graph has (2r + 1) ln (Δr) approximation ratio, where Δr is the largest cardinality among all r-hop neighborhoods in the network. The simulation results show that our algorithms are efficient.

On-line algorithms for the dominating set problem

1997 ◽  
Vol 61 (1) ◽  
pp. 11-14 ◽  
Author(s):  
Gow-Hsing King ◽  
Wen-Guey Tzeng
Keyword(s):  
Dominating Set ◽  
On Line ◽  
Dominating Set Problem

scholarly journals Independent dominating set problem revisited

2015 ◽  
Vol 562 ◽  
pp. 1-22 ◽  
Author(s):  
Ching-Hao Liu ◽  
Sheung-Hung Poon ◽  
Jin-Yong Lin
Keyword(s):  
Dominating Set ◽  
Dominating Set Problem ◽  
Independent Dominating Set
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