## Connected Dominating Set: Theory and ApplicationsThe connected dominating set has been a classic subject studied in graph theory since 1975. Since the 1990s, it has been found to have important applications in communication networks, especially in wireless networks, as a virtual backbone. Motivated from those applications, many papers have been published in the literature during last 15 years. Now, the connected dominating set has become a hot research topic in computer science. In this book, we are going to collect recent developments on the connected dominating set, which presents the state of the art in the study of connected dominating sets. The book consists of 16 chapters. Except the 1st one, each chapter is devoted to one problem, and consists of three parts, motivation and overview, problem complexity analysis, and approximation algorithm designs, which will lead the reader to see clearly about the background, formulation, existing important research results, and open problems. Therefore, this would be a very valuable reference book for researchers in computer science and operations research, especially in areas of theoretical computer science, computer communication networks, combinatorial optimization, and discrete mathematics. |

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### Contents

1 | |

Theory and Applications Chapter
2 CDS in General Graph | 11 |

Theory and Applications Chapter
3 CDS in Unit Disk Graph | 35 |

Theory and Applications Chapter 4 CDS in Unit Ball Graphs and Growth Bounded Graphs
| 63 |

Theory and Applications Chapter
5 Weighted CDS in Unit Disk Graph | 76 |

Theory and Applications Chapter
6 Coverage | 105 |

Theory and Applications Chapter
7 RoutingCost Constrained CDS | 119 |

Theory and Applications Chapter
8 CDS in DiskContainment Graphs | 133 |

Theory and Applications Chapter 9 CDS in DiskIntersection Graphs
| 150 |

Theory and Applications Chapter
10 Geometric Hitting Set and Disk Cover | 161 |

Theory and Applications Chapter
11 MinimumLatency Scheduling | 168 |

Theory and Applications Chapter
12 CDS in Planar Graphs | 183 |

193 | |

200 | |

### Other editions - View all

Connected Dominating Set: Theory and Applications Ding-Zhu Du,Peng-Jun Wan No preview available - 2014 |

### Common terms and phrases

approximation algorithm assume bipartite graph black vertices choose claim holds color compute connected component Connected Dominating Set connected domination number connector Consider construct contains contradiction Deﬁne degenerate quadruple denote disjoint disk1 disk1(v diskl edge endpoint exists ﬁrst gray neighbors Greedy Algorithm greedy approximation growth-bounded graphs hence horizontal strips independence number independent points input graph iteration k-tight least Lemma LOCAL(e lower disk maximal independent set MIN-CDS with constraint MIN-SET-COVER minimum CDS MINW-DS NODE-WEIGHTED STEINER TREE NP-hard number of vertices Opt(e optimal solution partition performance ratio phase planar graph polynomial-time Proof PTAS radius schedule sensor cover set cover shortest path simplex simplicial complex slots spanning tree Springer Science+Business Media Subcase subgraph submodular subset Suppose sweep line targets Theorem total weight unit disk graph upper bound upper disk virtual backbone Voronoi cell white vertex wireless networks βρ