All-to-all broadcast problems on Cartesian product graphs

Chang, Fei-Huang; Chia, Ma-Lian; Kuo, Dong‐Hau; Liaw, Shu Liang; Ling, Jen-Chun

doi:10.1016/j.tcs.2015.10.002

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Level-disjoint Partitions Of Optimal Height1

Introduction1

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2018

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(2 citation statements)

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“…, S k have optimal height. Observe that if equality in (4) or equality in (5) for bipartite graphs holds for all vertices (up to the root vertex) in LDPs, then LDPs have optimal height. See examples on Figure 4(b) and on Figure 3.…”

Section: Level-disjoint Partitions Of Optimal Heightmentioning

confidence: 99%

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Modelling simultaneous broadcasting by level-disjoint partitions

Gregor

Škrekovski

Vukašinović

2018

Applied Mathematics and Computation

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Simultaneous broadcasting of multiple messages from the same source vertex in synchronous networks is considered under restrictions that each vertex receives at most one message in a unit time step, every received message can be sent out only in the next time step, no message is sent to already informed vertex. The number of outgoing messages in unrestricted, messages have unit length, and we assume full-duplex mode. In [9] we developed a concept of level-disjoint partitions to study simultaneous broadcasting under this model. In this work we consider the optimal number of level-disjoint partitions. We also provide a necessary condition in terms of eccentricity and girth on existence of k v-rooted level-disjoint partitions of optimal height. In particular, we provide a structural characterization of graphs admitting two level-disjoint partitions with the same root.

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Section: Level-disjoint Partitions Of Optimal Heightmentioning

confidence: 99%

“…Let us remark that without restricting the number of messages that each vertex can receive at a time, a vertex may receive enormous amount of data altogether from its neighbors, which can cause a delay [3,4,8]. The study of efficiency of the 1-in port models can be found in [1,2,12].…”

Section: Introductionmentioning

confidence: 99%