Cleaning Graphs with a Greedy Algorithm

Document Type

Presentation Abstract

Presentation Date

11-17-2008

Abstract

Following the decontamination metaphor for searching a graph, suppose every vertex and edge of a graph is initially contaminated, or 'dirty'. Brushes are placed on some vertices and at each step, a vertex is 'cleaned', whereupon it sends one brush along each dirty incident edge (cleaning those edges). Brushes may not traverse clean edges. The model presented is one where the edges and vertices are continually recontaminated, say by algae, so that cleaning is regarded as an on-going process. Ideally, the final configuration of brushes, after all vertices and edges have been cleaned, should be a viable starting configuration to clean the graph again. The minimum number of brushes needed to continually clean a graph is called the brush number and is NP-hard to determine in general. Thus, the main results of this talk will focus on determining the (asymptotic) brush number of random regular graphs using a greedy algorithm.

Additional Details

Monday, 17 November 2008
3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109

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