Approximation Algorithms for the b-Edge Dominating Set Problem and Its Related Problems

2005 ◽  
pp. 747-756
Author(s):  
Takuro Fukunaga ◽  
Hiroshi Nagamochi
Keyword(s):  
Approximation Algorithms ◽  
Dominating Set ◽  
Edge Dominating Set ◽  
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.

scholarly journals New parameterized algorithms for the edge dominating set problem

2013 ◽  
Vol 511 ◽  
pp. 147-158 ◽  
Author(s):  
Mingyu Xiao ◽  
Ton Kloks ◽  
Sheung-Hung Poon
Keyword(s):  
Dominating Set ◽  
Parameterized Algorithms ◽  
Edge Dominating Set ◽  
Dominating Set Problem
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