Clean the graph before you draw it!

Authors:
Serge Gaspers;Margaret-Ellen Messinger;Richard J. Nowakowski;Paweł Prałat
Affiliations:
LIRMM -- University of Montpellier 2, CNRS, 34392 Montpellier, France;Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada;Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada;Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada
Venue:
Information Processing Letters
Year:
2009

Citing 8
Cited 4

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Balanced vertex-orderings of graphs

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Cleaning a network with brushes

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Cleaning Regular Graphs with Brushes

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Cleaning random d-regular graphs with brushes using a degree-greedy algorithm

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Parallel cleaning of a network with brushes

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Imbalance is fixed parameter tractable

COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
POLISH-Let us play the cleaning game

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Abstract

We prove a relationship between the Cleaning problem and the Balanced Vertex-Ordering problem, namely that the minimum total imbalance of a graph equals twice the brush number of a graph. This equality has consequences for both problems. On one hand, it allows us to prove the NP-completeness of the Cleaning problem, which was conjectured by Messinger et al. [M.-E. Messinger, R.J. Nowakowski, P. Pralat, Cleaning a network with brushes, Theoret. Comput. Sci. 399 (2008) 191-205]. On the other hand, it also enables us to design a faster algorithm for the Balanced Vertex-Ordering problem [J. Kara, K. Kratochvil, D. Wood, On the complexity of the balanced vertex ordering problem, Discrete Math. Theor. Comput. Sci. 9 (1) (2007) 193-202].