Approximation Algorithms for Permanent Dominating Set Problem on Dynamic Networks

2017 ◽  
pp. 265-279 ◽  
Author(s):  
Subhrangsu Mandal ◽  
Arobinda Gupta
Keyword(s):  
Approximation Algorithms ◽  
Dominating Set ◽  
Dynamic Networks ◽  
Dominating Set Problem

Minimum Dominating Set Problem for Unit Disks Revisited

2015 ◽  
Vol 25 (03) ◽  
pp. 227-244 ◽  
Author(s):  
Paz Carmi ◽  
Gautam K. Das ◽  
Ramesh K. Jallu ◽  
Subhas C. Nandy ◽  
Prajwal R. Prasad ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Time Complexity ◽  
Dominating Set ◽  
Minimum Dominating Set ◽  
Shifting Lemma ◽  
Dominating Set Problem ◽  
Unit Disks ◽  
A Minor ◽  
Text Unit

In this article, we study approximation algorithms for the problem of computing minimum dominating set for a given set [Formula: see text] of [Formula: see text] unit disks in [Formula: see text]. We first present a simple [Formula: see text] time 5-factor approximation algorithm for this problem, where [Formula: see text] is the size of the output. The best known 4-factor and 3-factor approximation algorithms for the same problem run in time [Formula: see text] and [Formula: see text] respectively [M. De, G. K. Das, P. Carmi and S. C. Nandy, Approximation algorithms for a variant of discrete piercing set problem for unit disks, Int. J. of Computational Geometry and Appl., 22(6):461–477, 2013]. We show that the time complexity of the in-place 4-factor approximation algorithm for this problem can be improved to [Formula: see text]. A minor modification of this algorithm produces a [Formula: see text]-factor approximation algorithm in [Formula: see text] time. The same techniques can be applied to have a 3-factor and a [Formula: see text]-factor approximation algorithms in time [Formula: see text] and [Formula: see text] respectively. Finally, we propose a very important shifting lemma, which is of independent interest, and it helps to present [Formula: see text]-factor approximation algorithm for the same problem. It also helps to improve the time complexity of the proposed PTAS for the problem.

ALGORITHMS FOR MINIMUM CONNECTED CAPACITATED DOMINATING SET PROBLEM

2011 ◽  
Vol 03 (01) ◽  
pp. 9-15 ◽  
Author(s):  
WEIPING SHANG ◽  
XIUMEI WANG
Keyword(s):  
Wireless Sensor Network ◽  
Approximation Algorithms ◽  
Sensor Network ◽  
Dominating Set ◽  
Connected Dominating Set ◽  
Wireless Sensor ◽  
Virtual Backbone ◽  
Dominating Set Problem

Connected dominating set (CDS) has been proposed as the virtual backbone to alleviate the broadcasting storm in wireless sensor network. Most recent research has extensively focused on the construction of connected dominating set. However, the nodes in the CDS need to dominate all its neighbors, and then some nodes cover a large number of neighboring nodes. Therefore, it is desirable to construct a capacitated dominating set, each node can dominate only a certain number of neighbors. In this paper, we study capacitated dominating set and connected capacitated dominating set, and propose two approximation algorithms with small approximation ratios.

MINIMUM CONNECTED r-HOP k-DOMINATING SET IN WIRELESS NETWORKS

2009 ◽  
Vol 01 (01) ◽  
pp. 45-57 ◽  
Author(s):  
DEYING LI ◽  
LIN LIU ◽  
HUIQIANG YANG
Keyword(s):  
Wireless Networks ◽  
Undirected Graph ◽  
Dominating Set ◽  
Approximation Ratio ◽  
Dominating Set Problem ◽  
Simulation Results

In this paper, we study the connected r-hop k-dominating set problem in wireless networks. We propose two algorithms for the problem. We prove that algorithm I for UDG has (2r + 1)3 approximate ratio for k ≤ (2r + 1)2 and (2r + 1)((2r + 1)2 + 1)-approximate ratio for k > (2r + 1)2. And algorithm II for any undirected graph has (2r + 1) ln (Δr) approximation ratio, where Δr is the largest cardinality among all r-hop neighborhoods in the network. The simulation results show that our algorithms are efficient.

On-line algorithms for the dominating set problem

1997 ◽  
Vol 61 (1) ◽  
pp. 11-14 ◽  
Author(s):  
Gow-Hsing King ◽  
Wen-Guey Tzeng
Keyword(s):  
Dominating Set ◽  
On Line ◽  
Dominating Set Problem
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