This paper is devoted to the gossip (or all-to-all) problem in the chordal ring under the one-port line model. The line model assumes long distance calls between non neighboring processors. In this sense, the line model is strongly related to circuit-switched networks, wormhole routing, optical networks supporting wavelength division multiplexing, ATM switching, and networks supporting connected mode routing protocols. Since the chordal rings are competitors of networks as meshes or tori

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... of theirs short diameter and bounded degree, it is of interest to ask whether they can support intensive c o m m unications (typically all-to-all) as e ciently as these networks. We p r o p o s e polynomial algorithms to derive optimal or near optimal gossip protocols in the chordal ring. Basic concepts An interconnection network is modeled by a connected undirected graph G = ( V E), where the vertices in V correspond to the processors, and the edges in E represent the communication links of the network. Our gossip algorithms are based on the so-called 3-phase gossip method 15]. For that purpose, the Section 3 gives a decomposition of the chordal ring into disjoint cycles.