Liar’s Dominating Set in Unit Disk Graphs

2018 ◽  
pp. 516-528 ◽  
Author(s):  
Ramesh K. Jallu ◽  
Sangram K. Jena ◽  
Gautam K. Das
Keyword(s):  
Unit Disk ◽  
Dominating Set ◽  
Unit Disk Graphs

ROMAN DOMINATION AND ITS VARIANTS IN UNIT DISK GRAPHS

2010 ◽  
Vol 02 (01) ◽  
pp. 99-105 ◽  
Author(s):  
WEIPING SHANG ◽  
XIUMEI WANG ◽  
XIAODONG HU
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Wireless Ad Hoc Networks ◽  
Ad Hoc ◽  
Dominating Set ◽  
Roman Domination ◽  
Intersection Graphs ◽  
Unit Disk Graphs ◽  
Np Complete ◽  
Hoc Networks

Unit disk graphs are the intersection graphs of equal sized disks in the plane, they are widely used as a mathematical model for wireless ad-hoc networks and some problems in computational geometry. In this paper we first show that Roman dominating set and connected Roman dominating set problems in unit disk graphs are NP-complete, and then present two approximation algorithms for these problems.

A PTAS for the minimum weighted dominating set problem with smooth weights on unit disk graphs

2010 ◽  
Vol 23 (4) ◽  
pp. 443-450 ◽  
Author(s):  
Xu Zhu ◽  
Wei Wang ◽  
Shan Shan ◽  
Zhong Wang ◽  
Weili Wu
Keyword(s):  
Unit Disk ◽  
Dominating Set ◽  
Unit Disk Graphs ◽  
Dominating Set Problem ◽  
Smooth Weights

Liar’s dominating set problem on unit disk graphs

2020 ◽  
Vol 286 ◽  
pp. 91-99 ◽  
Author(s):  
Ramesh K. Jallu ◽  
Gautam K. Das
Keyword(s):  
Unit Disk ◽  
Dominating Set ◽  
Unit Disk Graphs ◽  
Dominating Set Problem
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