Abstract
Imagine a large building with many corridors. A robot cleans these corridors in a greedy fashion, the next corridor cleaned is always the dirtiest to which it is adjacent. We determine bounds on the minimum s(G) and maximum S(G) number of time steps (over all edge weightings) before every edge of a graph G has been cleaned. We show that Eulerian graphs have a self-stabilizing property that holds for any initial edge weighting: after the initial cleaning of all edges, all subsequent cleanings require s(G) time steps. Finally, we show the only self-stabilizing trees are a subset of the superstars.
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Messinger, ME., Nowakowski, R.J. (2008). The Robot Cleans Up. In: Yang, B., Du, DZ., Wang, C.A. (eds) Combinatorial Optimization and Applications. COCOA 2008. Lecture Notes in Computer Science, vol 5165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85097-7_29
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DOI: https://doi.org/10.1007/978-3-540-85097-7_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85096-0
Online ISBN: 978-3-540-85097-7
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