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Connected Dominating Set

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 155 Accesses

Years and Authors of Summarized Original Work

  • 2003; Cheng, Huang, Li, Wu, Du

Problem Definition

Consider a graph G = (V, E). A subset C of V is called a dominating set if every vertex is either in C or adjacent to a vertex in C. If, furthermore, the subgraph induced by C is connected, then C is called a connected dominating set. A connected dominating set with a minimum cardinality is called a minimum connected dominating set (MCDS). Computing an MCDS is an NP-hard problem and there is no polynomial-time approximation with performance ratio \(\rho H(\Delta )\) for ρ < 1 unless \(\mathit{NP} \subseteq \mathit{DTIME}(n^{O(\ln \ \ln \ n)})\) where H is the harmonic function and \(\Delta\) is the maximum degree of the input graph [11].

A unit disk is a disk with radius one. A unit disk graph (UDG) is associated with a set of unit disks in the Euclidean plane. Each node is at the center of a unit disk. An edge exists between two nodes u and v if and only if \(\vert \mathit{uv}\vert \leq 1\)...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Mathematical Science and Applied Computing, Arizona State University at the West Campus, Phoenix, AZ, USA

    Feng Wang

  2. Computer Science, University of Minnesota, 200 Union Street S.E., 55455, Minneapolis, MN, USA

    Ding-Zhu Du

  3. Department of Computer Science, The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  4. Department of Computer Science, George Washington University, Washington, DC, USA

    Xiuzhen Cheng

Authors
  1. Feng Wang
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  2. Ding-Zhu Du
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  3. Xiuzhen Cheng
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Corresponding author

Correspondence to Feng Wang .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Wang, F., Du, DZ., Cheng, X. (2016). Connected Dominating Set. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_89

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