scholarly journals Swarm intelligence, exact and matheuristic approaches for minimum weight directed dominating set problem

2022 ◽  
Vol 109 ◽  
pp. 104647
Author(s):  
Mallikarjun Rao Nakkala ◽  
Alok Singh ◽  
André Rossi
Keyword(s):  
Swarm Intelligence ◽  
Dominating Set ◽  
Minimum Weight ◽  
Dominating Set Problem

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.

Sign in / Sign up

Export Citation Format

Share Document