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Periodic gossiping on trees. (English) Zbl 0836.68085
Summary: In periodic gossip schemes, the calls are periodically repeated according to a proper coloring of the edges of the underlying graph with integers $$1, 2, \dots, c$$. One period consists of $$c$$ consecutive rounds $$1, \dots, c$$ each containing time-parallel bidirectional calls on all edges with the same color. The problem is to design colorings which minimize the number of periods until gossiping is completed. We present an algorithm yielding “reasonable” colorings for trees, and discuss cases where it produces an optimal coloring. For these cases, the periodic gossip time, i.e. the minimum number of periods can be computed from the algorithm.

##### MSC:
 68R10 Graph theory (including graph drawing) in computer science 05C05 Trees 05C15 Coloring of graphs and hypergraphs 94C15 Applications of graph theory to circuits and networks
##### Keywords:
periodic gossip schemes
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##### References:
 [1] Liestman, A.L.; Richards, D., Network communication in edge-colored graphs: gossiping, IEEE trans. parallel distrib. systems, 4, 438-445, (1993)
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