NP-Completeness of the Independent Dominating Set Problem in the Class of Cubic Planar Bipartite Graphs

2020 ◽  
Vol 14 (2) ◽  
pp. 353-368
Author(s):  
Ya. A. Loverov ◽  
Yu. L. Orlovich
Keyword(s):  
Dominating Set ◽  
Bipartite Graphs ◽  
Np Completeness ◽  
Dominating Set Problem ◽  
Independent Dominating Set

scholarly journals Independent dominating set problem revisited

2015 ◽  
Vol 562 ◽  
pp. 1-22 ◽  
Author(s):  
Ching-Hao Liu ◽  
Sheung-Hung Poon ◽  
Jin-Yong Lin
Keyword(s):  
Dominating Set ◽  
Dominating Set Problem ◽  
Independent Dominating Set

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.

A memetic algorithm for minimum independent dominating set problem

2017 ◽  
Vol 30 (8) ◽  
pp. 2519-2529 ◽  
Author(s):  
Yiyuan Wang ◽  
Jiejiang Chen ◽  
Huanyao Sun ◽  
Minghao Yin
Keyword(s):  
Memetic Algorithm ◽  
Dominating Set ◽  
Dominating Set Problem ◽  
Independent Dominating Set

A path cost-based GRASP for minimum independent dominating set problem

2016 ◽  
Vol 28 (S1) ◽  
pp. 143-151 ◽  
Author(s):  
Yiyuan Wang ◽  
Ruizhi Li ◽  
Yupeng Zhou ◽  
Minghao Yin
Keyword(s):  
Dominating Set ◽  
Path Cost ◽  
Dominating Set Problem ◽  
Independent Dominating Set
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