Analyzing the Co-Movements of the US Gross State Product Growth with the Use of the Minimum Dominating Set

2014 ◽  
Author(s):  
Theophilos Papadimitriou ◽  
Periklis Gogas ◽  
Georgios Sarantitis
Keyword(s):  
Dominating Set ◽  
Minimum Dominating Set ◽  
The Us ◽  
Gross State Product

Energy-Efficient Sleep Scheduling in WBANs: From the Perspective of Minimum Dominating Set

2019 ◽  
Vol 6 (4) ◽  
pp. 6237-6246 ◽  
Author(s):  
Rongrong Zhang ◽  
Amiya Nayak ◽  
Shurong Zhang ◽  
Jihong Yu
Keyword(s):  
Energy Efficient ◽  
Dominating Set ◽  
Sleep Scheduling ◽  
Minimum Dominating Set

Analysis of Network Topology Using the Threshold-Minimum Dominating Set

2014 ◽  
Author(s):  
Theophilos Papadimitriou ◽  
Periklis Gogas ◽  
Georgios Sarantitis ◽  
Maria Matthaiou
Keyword(s):  
Network Topology ◽  
Dominating Set ◽  
Minimum Dominating Set

scholarly journals Two-goal Local Search and Inference Rules for Minimum Dominating Set

2020 ◽  
Author(s):  
Shaowei Cai ◽  
Wenying Hou ◽  
Yiyuan Wang ◽  
Chuan Luo ◽  
Qingwei Lin
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Inference Rules ◽  
Local Search Algorithm ◽  
Minimum Dominating Set ◽  
Massive Graphs ◽  
Construction Procedure ◽  
Almost All ◽  
Main Ideas

Minimum dominating set (MinDS) is a canonical NP-hard combinatorial optimization problem with applications. For large and hard instances one must resort to heuristic approaches to obtain good solutions within reasonable time. This paper develops an efficient local search algorithm for MinDS, which has two main ideas. The first one is a novel local search framework, while the second is a construction procedure with inference rules. Our algorithm named FastDS is evaluated on 4 standard benchmarks and 3 massive graphs benchmarks. FastDS obtains the best performance for almost all benchmarks, and obtains better solutions than state-of-the-art algorithms on massive graphs.

scholarly journals A Note on Total and Paired Domination of Cartesian Product Graphs

10.37236/2535 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
K. Choudhary ◽  
S. Margulies ◽  
I. V. Hicks
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Cartesian Product ◽  
Minimum Dominating Set ◽  
Cartesian Product Of Graphs ◽  
Product Graphs ◽  
Cartesian Product Graphs ◽  
Paired Domination ◽  
Product Of Graphs

A dominating set $D$ for a graph $G$ is a subset of $V(G)$ such that any vertex not in $D$ has at least one neighbor in $D$. The domination number $\gamma(G)$ is the size of a minimum dominating set in G. Vizing's conjecture from 1968 states that for the Cartesian product of graphs $G$ and $H$, $\gamma(G)\gamma(H) \leq \gamma(G \Box H)$, and Clark and Suen (2000) proved that $\gamma(G)\gamma(H) \leq 2 \gamma(G \Box H)$. In this paper, we modify the approach of Clark and Suen to prove a variety of similar bounds related to total and paired domination, and also extend these bounds to the $n$-Cartesian product of graphs $A^1$ through $A^n$.

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