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Exact Algorithms for Dominating Set

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  • First Online:
Encyclopedia of Algorithms

  • 211 Accesses

Years and Authors of Summarized Original Work

  • 2005; Fomin, Grandoni, Kratsch

  • 2008; van Rooij, Bodlaender

  • 2011; Iwata

Problem Definition

The dominating set problem is a classical NP-hard optimization problem which fits into the broader class of covering problems. Hundreds of papers have been written on this problem that has a natural motivation in facility location.

Definition 1

For a given undirected, simple graph G = (V, E), a subset of vertices \(D \subseteq V\) is called a dominating set if every vertex u ∈ V − D has a neighbor in D. The minimum dominating set problem (abbr. MDS) is to find a minimum dominating set of G, i.e., a dominating set of G of minimum cardinality.

Problem 1 (MDS)

Input: Undirected simple graph G = (V, E).

Output: A minimum dominating set D of G.

Various modifications of the dominating set problem are of interest, some of them obtained by putting additional constraints on the dominating set as, e.g., requesting it to be an independent set or to be connected....

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Recommended Reading

  1. Eppstein D (2006) Quasiconvex analysis of backtracking algorithms. ACM Trans Algorithms 2(4):492–509

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  2. Fomin FV, Grandoni F, Kratsch D (2005) Measure and conquer: domination – a case study. In: Proceedings of ICALP 2005, Lisbon

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  3. Fomin FV, Grandoni F, Kratsch D (2009) A measure & conquer approach for the analysis of exact algorithms. J ACM 56(5)

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  4. Fomin FV, Kratsch D (2010) Exact exponential algorithms. Springer, Heidelberg

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  5. Fomin FV, Kratsch D, Woeginger GJ (2004) Exact (exponential) algorithms for the dominating set problem. In: Proceedings of WG 2004, Bonn. LNCS, vol 3353. Springer, pp 245–256

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  6. Grandoni F (2004) Exact algorithms for hard graph problems. PhD thesis, Università di Roma “Tor Vergata”, Roma, Mar 2004

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  7. Iwata Y (2011) A faster algorithm for Dominating Set analyzed by the potential method. In: Proceedings of IPEC 2011, Saarbrücken. LNCS, vol 7112. Springer, pp 41–54

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  8. Nederlof J, van Rooij JMM, van Dijk TC (2014) Inclusion/exclusion meets measure and conquer. Algorithmica 69(3):685–740

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  10. van Rooij JMM (2011) Exact exponential-time algorithms for domination problems in graphs. PhD thesis, University Utrecht

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  11. van Rooij JMM, Bodlaender HL (2011) Exact algorithms for dominating set. Discret Appl Math 159(17):2147–2164

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Author information

Authors and Affiliations

  1. UFM MIM – LITA, Université de Lorraine, 57045, Metz, France

    Dieter Kratsch

Authors
  1. Dieter Kratsch
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Corresponding author

Correspondence to Dieter Kratsch .

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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© 2016 Springer Science+Business Media New York

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Kratsch, D. (2016). Exact Algorithms for Dominating Set. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_132

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