The Connected Domination Number of Grids
Adarsh Srinivasan,N. S. Narayanaswamy +1 more
- pp 247-258
TLDR
In this article, a new lower bound for Open image in new window for arbitrary m,n,n \ge 4 was obtained for grids with up to 4 rows and with 6 rows.Abstract:
Closed form expressions for the domination number of an \(n \times m\) grid have attracted significant attention, and an exact expression has been obtained in 2011 [7]. In this paper, we present our results on obtaining new lower bounds on the connected domination number of an \(n \times m\) grid. The problem has been solved for grids with up to 4 rows and with 6 rows and the best currently known lower bound for arbitrary m, n is Open image in new window [11]. Fujie [4] came up with a general construction for a connected dominating set of an \(n \times m\) grid. In this paper, we investigate whether this construction is indeed optimum. We prove a new lower bound of Open image in new window for arbitrary \(m,n \ge 4\).read more
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Connected domination in grid graphs.
Masahisa Goto,Koji M. Kobayashi +1 more
TL;DR: In this article, the minimum cardinality of a connected dominating set, called the connected domination number (CDP), of an undirected simple graph was determined for any $m \times n$ grid graph.
References
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Approximating Maximum Leaf Spanning Trees in Almost Linear Time
Hsueh-I Lu,R. Ravi +1 more
TL;DR: This paper gives a new greedy 3-approximation algorithm for maximum leaf spanning trees, where the running timeO((m+n)?(m,n)) required by the algorithm, where m is the number of edges and n is thenumber of nodes, is almost linear in the size of the graph.
Journal ArticleDOI
The Domination Number of Grids
TL;DR: The calculation of the domination number of all (n,m) grid graphs is concluded and Chang’s conjecture is proved saying that for every 16≤n≤m, γ(Gn, m) =⌊(n+2)(m+2)5⌋-4.5.
Journal ArticleDOI
A short note on the approximability of the maximum leaves spanning tree problem
TL;DR: It is proved that the NP-hard problem of finding in an undirected graph G a spanning tree with a maximum number of leaves is MAX-SNP hard, giving therefore a negative answer to this question, which was left open in [6].
Journal ArticleDOI
An exact algorithm for the maximum leaf spanning tree problem
TL;DR: A branch-and-bound algorithm is proposed for MLSTP, in which an upper bound is obtained by solving a minimum spanning tree problem by solving the minimum number of leaves.
Journal ArticleDOI
A 2-Approximation Algorithm for Finding a Spanning Tree with Maximum Number of Leaves
TL;DR: A simple, linear time 2-approximation algorithm for this problem, improving on the previous best known algorithm for the problem, which has approximation ratio 3.