Results 11 to 20 of about 490,847 (283)
Operations Research Letters, 2004 This paper presents several representation theorems for the solubility of three cost allocation problems, which are presented as cooperative games. In each problem, a graph \(G = (V, E)\) is given along with a cost function: given \(S \subseteq V\), \(c(S)\) is the cost of \(k\)-dominating the vertices in \(S\), i.e., building a set \(K \subseteq V ...
Velzen, S. van
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The complexity of dominating set reconfiguration [PDF]
Theoretical Computer Science, 2015 Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such that each dominating set in the sequence is of cardinality at most $k$ and can be obtained from the previous one by ...
Arash Haddadan +6 more
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Reconfiguration of Dominating Sets [PDF]
Journal of Combinatorial Optimization, 2014 12 pages, 4 ...
Akira Suzuki 0001 +2 more
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Distributed dominating sets on grids [PDF]
2013 American Control Conference, 2013 10 pages, 9 figures, accepted in ACC ...
Elaheh Fata +2 more
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A Linear Kernel for Planar Total Dominating Set [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 A total dominating set of a graph $G=(V,E)$ is a subset $D \subseteq V$ such that every vertex in $V$ is adjacent to some vertex in $D$. Finding a total dominating set of minimum size is NP-hard on planar graphs and W[2]-complete on general graphs when ...
Valentin Garnero, Ignasi Sau
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Dominating Sets and Connected Dominating Sets in Dynamic Graphs [PDF]
CoRR, 2019 In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set. For those two problems, we present algorithms that maintain a solution under edge insertions and edge deletions in time $O(Δ\cdot \text{polylog}~n)$ per update, where $Δ$ is the maximum vertex degree in the ...
Hjuler N. +3 more
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Dominating Sets and Domination Polynomials of Paths [PDF]
International Journal of Mathematics and Mathematical Sciences, 2009 Let G = (V, E) be a simple graph. A set S⊆V is a dominating set of G, if every vertex in V\S is adjacent to at least one vertex in S. Let be the family of all dominating sets of a path Pn with cardinality i, and let . In this paper, we construct , and obtain a recursive formula for d(Pn, i).
Saeid Alikhani, Yee-Hock Peng
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CoRR, 2022 We consider a minimizing variant of the well-known \emph{No-Three-In-Line Problem}, the \emph{Geometric Dominating Set Problem}: What is the smallest number of points in an $n\times n$~grid such that every grid point lies on a common line with two of the points in the set?
Oswin Aichholzer +2 more
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On redundant locating-dominating sets
Discrete Applied Mathematics, 2023 A locating-dominating set in a graph G is a subset of vertices representing "detectors" which can locate an "intruder" given that each detector covers its closed neighborhood and can distinguish its own location from its neighbors. We explore a fault-tolerant variant of locating-dominating sets called redundant locating-dominating sets, which can ...
Devin C. Jean, Suk Jai Seo
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