scholarly journals Minimum Connected Dominating Sets of Random Cubic Graphs

10.37236/1624 ◽  
2002 ◽  
Vol 9 (1) ◽  
Author(s):  
W. Duckworth
Keyword(s):  
Differential Equations ◽  
Greedy Algorithm ◽  
Dominating Set ◽  
Connected Dominating Set ◽  
Cubic Graphs ◽  
Dominating Sets ◽  
Connected Dominating Sets ◽  
Average Case ◽  
Simple Heuristic

We present a simple heuristic for finding a small connected dominating set of cubic graphs. The average-case performance of this heuristic, which is a randomised greedy algorithm, is analysed on random $n$-vertex cubic graphs using differential equations. In this way, we prove that the expected size of the connected dominating set returned by the algorithm is asymptotically almost surely less than $0.5854n$.

New Self-Stabilizing Algorithms for Minimal Weakly Connected Dominating Sets

2015 ◽  
Vol 26 (02) ◽  
pp. 229-240
Author(s):  
Yihua Ding ◽  
James Z. Wang ◽  
Pradip K. Srimani
Keyword(s):  
Connected Graph ◽  
Dominating Set ◽  
Graph Algorithm ◽  
Connected Dominating Set ◽  
Dominating Sets ◽  
Time And Space ◽  
Stabilization Time ◽  
Connected Dominating Sets ◽  
Space Requirement ◽  
Weakly Connected Dominating Set

In this paper, we propose two new self-stabilizing algorithms, MWCDS-C and MWCDS-D, for minimal weakly connected dominating sets in an arbitrary connected graph. Algorithm MWCDS-C stabilizes in O(n4) steps using an unfair central daemon and space requirement at each node is O(log n) bits at each node for an arbitrary connected graph with n nodes; it uses a designated node while other nodes are identical and anonymous. Algorithm MWCDS-D stabilizes using an unfair distributed daemon with identical time and space complexities, but it assumes unique node IDs. In the literature, the best reported stabilization time for a minimal weakly connected dominating set algorithm is O(nmA) under a distributed daemon [1], where m is the number of edges and A is the number of moves to construct a breadth-first tree.

scholarly journals On the doubly connected domination number of a graph

2006 ◽  
Vol 4 (1) ◽  
pp. 34-45 ◽  
Author(s):  
Joanna Cyman ◽  
Magdalena Lemańska ◽  
Joanna Raczek
Keyword(s):  
Connected Graph ◽  
Dominating Set ◽  
Domination Number ◽  
Connected Dominating Set ◽  
Dominating Sets ◽  
Connected Dominating Sets ◽  
Connected Domination Number

AbstractFor a given connected graph G = (V, E), a set $$D \subseteq V(G)$$ is a doubly connected dominating set if it is dominating and both 〈D〉 and 〈V (G)-D〉 are connected. The cardinality of the minimum doubly connected dominating set in G is the doubly connected domination number. We investigate several properties of doubly connected dominating sets and give some bounds on the doubly connected domination number.

Doubly connected domination in the join and Cartesian product of some graphs

2014 ◽  
Vol 07 (04) ◽  
pp. 1450054
Author(s):  
Benjier H. Arriola ◽  
Sergio R. Canoy
Keyword(s):  
Connected Graph ◽  
Dominating Set ◽  
Cartesian Product ◽  
Connected Dominating Set ◽  
Dominating Sets ◽  
Connected Dominating Sets ◽  
Restrained Domination ◽  
Total Restrained Domination ◽  
Positive Integers ◽  
Simple Connected Graph

Let G be a simple connected graph. A connected dominating set S ⊂ V(G) is called a doubly connected dominating set of G if the subgraph 〈V(G)\S〉 induced by V(G)\S is connected. We show that given any three positive integers a, b, and c with 4 ≤ a ≤ b ≤ c, where b ≤ 2a, there exists a connected graph G such that a = γr(G), b = γtr(G), and c = γcc(G), where γr, γtr, and γcc are, respectively, the restrained domination, total restrained domination, and doubly connected domination parameters. Also, we characterize the doubly connected dominating sets in the join of any graphs and Cartesian product of some graphs. The corresponding doubly connected domination numbers of these graphs are also determined.

scholarly journals New Computation of Resolving Connected Dominating Sets in Weighted Networks

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1174
Author(s):  
Adriana Dapena ◽  
Daniel Iglesia ◽  
Francisco J. Vazquez-Araujo ◽  
Paula M. Castro
Keyword(s):  
Complex Networks ◽  
Dominating Set ◽  
Connected Dominating Set ◽  
Virtual Backbone ◽  
Dominating Sets ◽  
Connected Subset ◽  
Resolving Set ◽  
Connected Dominating Sets ◽  
Minimum Cardinality ◽  
Information Interchange

In this paper we focus on the issue related to finding the resolving connected dominating sets (RCDSs) of a graph, denoted by G. The connected dominating set (CDS) is a connected subset of vertices of G selected to guarantee that all vertices in the graph are connected to vertices in the CDS. The connected dominating set with minimum cardinality, or minimum CDS (MCDS), is an adequate virtual backbone for information interchange in a network. When distinct vertices of G have also distinct representations with respect to a subset of vertices in the MCDS, it is said that the MCDS includes a resolving set (RS) of G. With this work, we explore different strategies to find the RCDS with minimum cardinality in complex networks where the vertices have different importances.

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%.

A SIMPLE HEURISTIC FOR MINIMUM CONNECTED DOMINATING SET IN GRAPHS

2003 ◽  
Vol 14 (02) ◽  
pp. 323-333 ◽  
Author(s):  
PENG-JUN WAN ◽  
KHALED M. ALZOUBI ◽  
OPHIR FRIEDER
Keyword(s):  
Planar Graph ◽  
Complete Graph ◽  
Dominating Set ◽  
Independence Number ◽  
Domination Number ◽  
Connected Dominating Set ◽  
Minimum Connected Dominating Set ◽  
Simple Heuristic ◽  
Connected Domination Number ◽  
A Minor

Let α2(G), γ(G) and γc(G) be the 2-independence number, the domination number, and the connected domination number of a graph G respectively. Then α2(G) ≤ γ (G) ≤ γc(G). In this paper , we present a simple heuristic for Minimum Connected Dominating Set in graphs. When running on a graph G excluding Km (the complete graph of order m) as a minor, the heuristic produces a connected dominating set of cardinality at most 7α2(G) - 4 if m = 3, or at most [Formula: see text] if m ≥ 4. In particular, if running on a planar graph G, the heuristic outputs a connected dominating set of cardinality at most 15α2(G) - 5.

scholarly journals Dominating Sets of Random 2-in 2-out Directed Graphs

10.37236/753 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Stephen Howe
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Upper Bound ◽  
Directed Graphs ◽  
Dominating Set ◽  
Dominating Sets

We analyse an algorithm for finding small dominating sets of $2$-in $2$-out directed graphs using a deprioritised algorithm and differential equations. This deprioritised approach determines an a.a.s. upper bound of $0.39856n$ on the size of the smallest dominating set of a random $2$-in $2$-out digraph on $n$ vertices. Direct expectation arguments determine a corresponding lower bound of $0.3495n$.

Sign in / Sign up

Export Citation Format

Share Document