Topic

# Dominating set

About: Dominating set is a research topic. Over the lifetime, 4058 publications have been published within this topic receiving 72432 citations. The topic is also known as: dominating set problem.

##### Papers published on a yearly basis

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01 Jan 1998

TL;DR: Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of domination multiproperty and multiset parameters sums and products of parameters dominating functions frameworks for domination domination complexity and algorithms are presented.

Abstract: Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of domination multiproperty and multiset parameters sums and products of parameters dominating functions frameworks for domination domination complexity and algorithms.

3,265 citations

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01 Jan 1998

TL;DR: A survey of domination-related parameters topics on directed graphs graphs can be found in this article with respect to the domination number bondage, insensitivity, and reinforcement of graph dominating functions.

Abstract: LP-duality, complementarity and generality of graphical subset parameters dominating functions in graphs fractional domination and related parameters majority domination and its generalizations convexity of external domination-related functions of graphs combinatorial problems on chessboards - II domination in cartesian products - Vizing's conjecture algorithms complexity results domination parameters of a graph global domination distance domination in graphs domatic numbers of graphs and their variants - a survey domination-related parameters topics on domination in directed graphs graphs critical with respect to the domination number bondage, insensitivity and reinforcement.

1,289 citations

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Bell Labs

^{1}TL;DR: A general technique that can be used to obtain approximation algorithms for various NP-complete problems on planar graphs, which includes maximum independent set, maximum tile salvage, partition into triangles, maximum H-matching, minimum vertex cover, minimum dominating set, and minimum edge dominating set.

Abstract: This paper describes a general technique that can be used to obtain approximation schemes for various NP-complete problems on planar graphs. The strategy depends on decompos- ing a planar graph into subgraphs of a form we call k-outerplanar. For fixed k, the problems of interest are solvable optimally in linear time on k-outerplanar graphs by dynamic programming. For general planar graphs, if the problem is a maximization problem, such as maximum independent set, this technique gives for each k a linear time algorithm that produces a solution whose size is at least k/(k + 1)optimal. If the problem is a minimization problem, such as minimum vertex cover, it gives for each k a linear time algorithm that produces a solution whose size is at most (k + 1)/k optimal. Taking k = (c log log nl or k = (c log nl, where n is the number of nodes and c is some constant, we get polynomial time approximation algorithms whose solution sizes converge toward optimal as n increases. The class of problems for which this approach provides approximation schemes includes maximum independent set, maximum tile salvage, partition into triangles, maximum H-matching, minimum vertex cover, minimum dominat- ing set, and minimum edge dominating set. For these and certain other problems, the proof of solvability on k-outerplanar graphs also enlarges the class of planar gmphs for which the problems are known to be solvable in polynomial time.

1,047 citations

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26 Mar 2000TL;DR: A heuristic to form d-clusters in a wireless ad hoc network that tends to re-elect existing clusterheads even when the network configuration changes and has a tendency to evenly distribute the mobile nodes among the clusterheads, and evently distribute the responsibility of acting as clusterheads among all nodes.

Abstract: An ad hoc network may be logically represented as a set of clusters. The clusterheads form a d-hop dominating set. Each node is at most d hops from a clusterhead. Clusterheads form a virtual backbone and may be used to route packets for nodes in their cluster. Previous heuristics restricted themselves to 1-hop clusters. We show that the minimum d-hop dominating set problem is NP-complete. Then we present a heuristic to form d-clusters in a wireless ad hoc network. Nodes are assumed to have a non-deterministic mobility pattern. Clusters are formed by diffusing node identities along the wireless links. When the heuristic terminates, a node either becomes a clusterhead, or is at most d wireless hops away from its clusterhead. The value of d is a parameter of the heuristic. The heuristic can be run either at regular intervals, or whenever the network configuration changes. One of the features of the heuristic is that it tends to re-elect existing clusterheads even when the network configuration changes. This helps to reduce the communication overheads during transition from old clusterheads to new clusterheads. Also, there is a tendency to evenly distribute the mobile nodes among the clusterheads, and evently distribute the responsibility of acting as clusterheads among all nodes. Thus, the heuristic is fair and stable. Simulation experiments demonstrate that the proposed heuristic is better than the two earlier heuristics, namely the LCA and degree-based solutions.

1,029 citations

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TL;DR: The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to be either in the dominating set, or adjacent to some vertex.

Abstract: The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to be either in the dominating set, or adjacent to some vertex i

1,026 citations