Parallel cleaning of a network with brushes

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, West Virginia University, Morgantown, WV 26506-6310, USA
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

We consider the process of cleaning a network where at each time step, all vertices that have at least as many brushes as incident, contaminated edges, send brushes down these edges and remove them from the network. An added condition is that, because of the contamination model used, the final configuration must be the initial configuration of another cleaning of the network. We find the minimum number of brushes required for trees, cycles, complete bipartite networks; and for all networks when all edges must be cleaned on each step. Finally, we give bounds on the number of brushes required for complete networks.