Abstract
Every node of an undirected connected graph is colored white or black. Adjacent nodes can be compared and the outcome of each comparison is either 0 (same color) or 1 (different colors). The aim is to discover a node of the majority color, or to conclude that there is the same number of black and white nodes. We consider randomized algorithms for this task and establish upper and lower bounds on their expected running time. Our main contribution are lower bounds showing that some simple and natural algorithms for this problem cannot be improved in general.
This work was done during the first author’s visit at the Research Chair in Distributed Computing of the Université du Québec en Outaouais. The work of the second author was supported in part by NSERC grant OGP 0008136 and by the Research Chair in Distributed Computing of the Université du Québec en Outaouais.
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De Marco, G., Pelc, A. (2003). Randomized Algorithms for Determining the Majority on Graphs. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_31
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DOI: https://doi.org/10.1007/978-3-540-45138-9_31
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