A hybrid algorithmic model for the minimum weight dominating set problem

2016 ◽  
Vol 64 ◽  
pp. 57-68 ◽  
Author(s):  
Salim Bouamama ◽  
Christian Blum
Keyword(s):  
Dominating Set ◽  
Minimum Weight ◽  
Dominating Set Problem ◽  
Algorithmic Model

A BETTER APPROXIMATION FOR MINIMUM AVERAGE ROUTING PATH CLUSTERING PROBLEM IN 2-D UNDERWATER SENSOR NETWORKS

2009 ◽  
Vol 01 (02) ◽  
pp. 175-191 ◽  
Author(s):  
WEI WANG ◽  
DONGHYUN KIM ◽  
JAMES WILLSON ◽  
BHAVANI THURAISINGHAM ◽  
WEILI WU
Keyword(s):  
Sensor Networks ◽  
Approximation Algorithm ◽  
Dominating Set ◽  
Minimum Weight ◽  
Performance Ratio ◽  
Underwater Sensor Networks ◽  
Clustering Problem ◽  
Np Completeness ◽  
Dominating Set Problem ◽  
Special Case

Previously, we proposed Minimum Average Routing Path Clustering Problem (MARPCP) in multi-hop USNs. The goal of this problem is to find a clustering of a USN so that the average clustering-based routing path from a node to it nearest underwater sink is minimized. We relaxed MARPCP to a special case of Minimum Weight Dominating Set Problem (MWDSP), namely MWDSP-R. In addition, we showed the Performance Ratio (PR) of α-approximation algorithm for MWDSP-R is 3α for MARPCP. Based on this result, we showed the existence of a (15 + ∊)-approximation algorithm for MARPCP. In this paper, we first establish the NP-completeness of both MARPCP and MWDSP-R. Then, we propose a PTAS for MWDSP-R. By combining this result with our previous one, we have a (3 + ∊)-approximation algorithm for MARPCP.

scholarly journals Independent sets in (P₆, diamond)-free graphs

2009 ◽  
Vol Vol. 11 no. 1 (Graph and Algorithms) ◽  
Author(s):  
Raffaele Mosca
Keyword(s):  
Polynomial Time ◽  
Dominating Set ◽  
Minimum Weight ◽  
Independent Set ◽  
Independent Sets ◽  
Maximum Weight ◽  
Independent Set Problem ◽  
International Audience ◽  
Dominating Set Problem ◽  
Independent Dominating Set

Graphs and Algorithms International audience We prove that on the class of (P6,diamond)-free graphs the Maximum-Weight Independent Set problem and the Minimum-Weight Independent Dominating Set problem can be solved in polynomial time.

scholarly journals Fault Tolerance and 2-Domination in Certain Interconnection Networks

2019 ◽  
Vol 11 (2) ◽  
pp. 181
Author(s):  
Lian Chen ◽  
Xiujun Zhang
Keyword(s):  
Fault Tolerance ◽  
Sensor Network ◽  
Interconnection Networks ◽  
Dominating Set ◽  
Minimum Weight ◽  
Domination Number ◽  
Dominating Set Problem ◽  
Dominating Function ◽  
Domination Numbers

A graph could be understood as a sensor network, in which the vertices represent the sensors and two vertices are adjacent if and only if the corresponding devices can communicate with each other. For a network G, a 2-dominating function on G is a function f : V(G) → [0, 1] such that each vertex assigned with 0 has at least two neighbors assigned with 1. The weight of f is Σ_u∈V(G) f (u), and the minimum weight over all 2-dominating functions is the 2-domination number of G. The 2-dominating set problem consists of finding the 2-domination number of a graph and it was proposed to model the fault tolerance of a sensor network. In this paper, we determined substantial 2-domination numbers of 2-dimensional meshes, cylinders, tori and hypercubes.

The Minimum Weight Dominating Set Problem under Hybrid Uncertain Environments

2014 ◽  
Vol 624 ◽  
pp. 545-548
Author(s):  
Chen Yin Wang ◽  
Dong Ling Luo ◽  
Mo Wei Zeng ◽  
Yang Yi ◽  
Xiao Cong Zhou
Keyword(s):  
Fuzzy Theory ◽  
Dominating Set ◽  
Minimum Weight ◽  
Intelligent Algorithm ◽  
Uncertain Environments ◽  
Hybrid Intelligent Algorithm ◽  
Fuzzy Variables ◽  
Uncertain Variables ◽  
Dominating Set Problem ◽  
Random Fuzzy Variables

The minimum weight dominating set problem (MWDSP) has been a popular research topic in recent years. The weights of vertexes may be considered as cost, time, or opponent’s payoff, which are uncertain in most cases. This paper discusses MWDSP under hybrid uncertain environments where the weights of vertexes are random fuzzy variables. First, random fuzzy theory is introduced to describe these hybrid uncertain variables. Then we propose three decision models based on three different decision criteria to solve MWDSP under hybrid uncertain environments. To solve the proposed models, we present a hybrid intelligent algorithm where random fuzzy simulation and genetic algorithm are embedded. Numerical experiments are performed in the last to show the robustness and effectiveness of the presented hybrid intelligent algorithm.

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