Analysis of Network Topology Using the Threshold-Minimum Dominating Set

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.

Download Full-text

A Note on Total and Paired Domination of Cartesian Product Graphs

The Electronic Journal of Combinatorics ◽

10.37236/2535 ◽

2013 ◽

Vol 20 (3) ◽

Cited By ~ 2

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 $A^n$.

Download Full-text

Heuristics for Generalized Minimum Dominating Set Problem

Advances in Intelligent Systems and Computing - Soft Computing: Theories and Applications ◽

10.1007/978-981-16-1696-9_29 ◽

2021 ◽

pp. 313-327

Author(s):

Mallikarjun Rao Nakkala ◽

Alok Singh

Keyword(s):

Dominating Set ◽

Minimum Dominating Set ◽

Dominating Set Problem

Download Full-text

Research on MPLS Network Topology Aggregation Algorithm With The Effective Connected Dominating Sets

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.155-156.1025 ◽

2012 ◽

Vol 155-156 ◽

pp. 1025-1029 ◽

Cited By ~ 1

Author(s):

Jing Feng ◽

Sheng Qian Ma ◽

Man Hong Fan ◽

Ke Ning Wang

Keyword(s):

Network Topology ◽

Dominating Set ◽

Dominating Sets ◽

Breadth First Search ◽

Label Switching ◽

Switching Path ◽

Topology Aggregation ◽

Multi Protocol Label Switching ◽

Network Topologies ◽

The Cost

Using dominating set can aggregate the complex physical network topologies into simple virtual topologies and reduce the cost of the networks. In the Multi-Protocol Label Switching (MPLS) network, the dominating set constructed based on label router can effectively aggregate MPLS network topology and reduce the amount of Label Switching Path (LSP), so as to save the expenses of network maintain information. However, simply considering the size of dominating set can't guarantee the best performance of the networks after aggregating. Therefore, an improved algorithm based on breadth-first search spanning tree is proposed, considering the size of the dominating set, bandwidth performance of the nodes and path length between nodes, which can effectively extend the MPLS network, with excellent bandwidth performance and reduce the data transmission delay.

Download Full-text