Combinatorial bounds via measure and conquer

2008 ◽  
Vol 5 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Fedor V. Fomin ◽  
Fabrizio Grandoni ◽  
Artem V. Pyatkin ◽  
Alexey A. Stepanov
Keyword(s):  
Measure And Conquer

Bounding the Number of Minimal Dominating Sets: A Measure and Conquer Approach

2005 ◽  
pp. 573-582 ◽  
Author(s):  
Fedor V. Fomin ◽  
Fabrizio Grandoni ◽  
Artem V. Pyatkin ◽  
Alexey A. Stepanov
Keyword(s):  
Dominating Sets ◽  
Measure And Conquer

scholarly journals Separate, Measure and Conquer

2017 ◽  
Vol 13 (4) ◽  
pp. 1-36 ◽  
Author(s):  
Serge Gaspers ◽  
Gregory B. Sorkin
Keyword(s):  
Measure And Conquer

Inclusion/Exclusion Meets Measure and Conquer

2009 ◽  
pp. 554-565 ◽  
Author(s):  
Johan M. M. van Rooij ◽  
Jesper Nederlof ◽  
Thomas C. van Dijk
Keyword(s):  
Measure And Conquer

scholarly journals Domination cover number of graphs

2019 ◽  
Vol 11 (02) ◽  
pp. 1950020
Author(s):  
M. Alambardar Meybodi ◽  
M. R. Hooshmandasl ◽  
P. Sharifani ◽  
A. Shakiba
Keyword(s):  
Real World ◽  
Dominating Set ◽  
Dominating Sets ◽  
Art Gallery ◽  
Art Gallery Problem ◽  
Measure And Conquer ◽  
Graph Classes ◽  
Block Graphs ◽  
New Criterion ◽  
Real World Problems

A set [Formula: see text] for the graph [Formula: see text] is called a dominating set if any vertex [Formula: see text] has at least one neighbor in [Formula: see text]. Fomin et al. [Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications, ACM Transactions on Algorithms (TALG) 5(1) (2008) 9] gave an algorithm for enumerating all minimal dominating sets with [Formula: see text] vertices in [Formula: see text] time. It is known that the number of minimal dominating sets for interval graphs and trees on [Formula: see text] vertices is at most [Formula: see text]. In this paper, we introduce the domination cover number as a new criterion for evaluating the dominating sets in graphs. The domination cover number of a dominating set [Formula: see text], denoted by [Formula: see text], is the summation of the degrees of the vertices in [Formula: see text]. Maximizing or minimizing this parameter among all minimal dominating sets has interesting applications in many real-world problems, such as the art gallery problem. Moreover, we investigate this concept for different graph classes and propose some algorithms for finding the domination cover number in trees and block graphs.

scholarly journals Measure and Conquer: Domination – A Case Study

2005 ◽  
pp. 191-203 ◽  
Author(s):  
Fedor V. Fomin ◽  
Fabrizio Grandoni ◽  
Dieter Kratsch
Keyword(s):  
Measure And Conquer
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