Exact (exponential) algorithms for the dominating set problem

Authors:
Fedor V. Fomin;Dieter Kratsch;Gerhard J. Woeginger
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway;LITA, Université de Metz, Metz Cedex 01, France;Department of Mathematics and Computer Science, TU Eindhoven, Eindhoven, The Netherlands
Venue:
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2004

Citing 8
Cited 30

What are the least tractable instances of max independent set?

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Which problems have strongly exponential complexity?

Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search

Theoretical Computer Science
Dominating sets in planar graphs: branch-width and exponential speed-up

SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Small Maximal Independent Sets and Faster Exact Graph Coloring

WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Exact algorithms for NP-hard problems: a survey

Combinatorial optimization - Eureka, you shrink!
Parameterized Complexity

Parameterized Complexity

Pathwidth of cubic graphs and exact algorithms

Information Processing Letters
An exact algorithm for the minimum dominating clique problem

Theoretical Computer Science
Finding a dominating set on bipartite graphs

Information Processing Letters
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number

CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications

ACM Transactions on Algorithms (TALG)
Efficiency in exponential time for domination-type problems

Discrete Applied Mathematics
Vertex and edge covers with clustering properties: Complexity and algorithms

Journal of Discrete Algorithms
A measure & conquer approach for the analysis of exact algorithms

Journal of the ACM (JACM)
A randomized algorithm for determining dominating sets in graphs of maximum degree five

Theoretical Computer Science
Exponential time algorithms for the minimum dominating set problem on some graph classes

ACM Transactions on Algorithms (TALG)
Pathwidth of cubic graphs and exact algorithms

Information Processing Letters
A hybrid graph representation for recursive backtracking algorithms

FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Solving capacitated dominating set by using covering by subsets and maximum matching

WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Exact algorithms for dominating set

Discrete Applied Mathematics
A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs

WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Solving connected dominating set faster than 2n

FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Exponential time algorithms for the minimum dominating set problem on some graph classes

SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Measure and conquer: domination – a case study

ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Bounding the number of minimal dominating sets: a measure and conquer approach

ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
An exact 2.9416n algorithm for the three domatic number problem

MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Algorithms based on the treewidth of sparse graphs

WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
An exact algorithm for the minimum dominating clique problem

IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
EDGE DOMINATING SET: efficient enumeration-based exact algorithms

IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Exact algorithms for finding the minimum independent dominating set in graphs

ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
A faster algorithm for dominating set analyzed by the potential method

IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Lower bounds on kernelization

Discrete Optimization
Performance analysis of virtual clusters in personal communication networks

Cluster Computing
Solving the minimum M-dominating set problem by a continuous optimization approach based on DC programming and DCA

Journal of Combinatorial Optimization
Counting minimum weighted dominating sets

COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Solving Capacitated Dominating Set by using covering by subsets and maximum matching

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We design fast exact algorithms for the problem of computing a minimum dominating set in undirected graphs. Since this problem is NP-hard, it comes with no big surprise that all our time complexities are exponential in the number n of vertices. The contribution of this paper are ‘nice’ exponential time complexities that are bounded by functions of the form cn with reasonably small constants cn. And for the special cases of split graphs, bipartite graphs, and graphs of maximum degree three, we reach time complexities of 1.41422n, 1.73206n, and 1.51433n, respectively.