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Modelling simultaneous broadcasting by level-disjoint partitions

Author

Listed:
  • Gregor, Petr
  • Škrekovski, Riste
  • Vukašinović, Vida

Abstract

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 vertices. The number of outgoing messages is unrestricted, messages have unit length, and we assume full-duplex mode. In Gregor et al. (2015), 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.

Suggested Citation

  • Gregor, Petr & Škrekovski, Riste & Vukašinović, Vida, 2018. "Modelling simultaneous broadcasting by level-disjoint partitions," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 15-23.
    • Handle: RePEc:eee:apmaco:v:325:y:2018:i:c:p:15-23
    DOI: 10.1016/j.amc.2017.12.018
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    References listed on IDEAS

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    1. Sun-Yuan Hsieh & Pei-Yu Yu, 2007. "Fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges," Journal of Combinatorial Optimization, Springer, vol. 13(2), pages 153-162, February.
    2. Gregor, Petr & Škrekovski, Riste & Vukašinović, Vida, 2015. "Rooted level-disjoint partitions of Cartesian products," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 244-258.
    3. Chang, Yu-Huei & Yang, Jinn-Shyong & Chang, Jou-Ming & Wang, Yue-Li, 2015. "A Fast Parallel Algorithm for Constructing Independent Spanning Trees on Parity Cubes," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 489-495.
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    Cited by:

    1. Petr Gregor & Riste Škrekovski & Vida Vukašinović, 2018. "Broadcasting multiple messages in the 1-in port model in optimal time," Journal of Combinatorial Optimization, Springer, vol. 36(4), pages 1333-1355, November.

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