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Network Communication in Edge-Colored Graphs: Gossiping
April 1993 (vol. 4 no. 4)
pp. 438-445

A mechanism for scheduling communications in a network in which individuals exchange information periodically according to a fixed schedule is presented. A proper kedge-coloring of the network is considered to be a schedule of allowed communicationssuch that an edge of color i can be used only at times i modulo k. Within thiscommunication scheduling mechanism, the information exchange problem known asgossiping is considered. It is proved that there is a proper k edge-coloring such thatgossip can be completed in a path of n edges in a certain time for ngreater than or equal to k greater than or equal to 1. Gossipcan not be completed in such a path any earlier under any proper k edge-coloring. In anytree of bounded degree Delta and diameter d, gossip can be completed under a properDelta edge-coloring in time ( Delta -1)d+1. In a k edge-colored cycle of n vertices, othertime requirements of gossip are determined.

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Index Terms:
Index Termsnetwork communication; edge-colored graphs; gossiping; scheduling communications;graph colouring; multiprocessor interconnection networks; scheduling
A.L. Liestman, D. Richards, "Network Communication in Edge-Colored Graphs: Gossiping," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 4, pp. 438-445, April 1993, doi:10.1109/71.219758
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