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Rooted level-disjoint partitions of Cartesian products

Author

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

Abstract

In interconnection networks one often needs to broadcast multiple messages in parallel from a single source so that the load at each node is minimal. With this motivation we study a new concept of rooted level-disjoint partitions of graphs. In particular, we develop a general construction of level-disjoint partitions for Cartesian products of graphs that is efficient both in the number of level partitions as in the maximal height. As an example, we show that the hypercube Q n for every dimension n=3·2i or n=4·2i where i ≥ 0 has n level-disjoint partitions with the same root and with maximal height 3n−2. Both the number of such partitions and the maximal height are optimal. Moreover, we conjecture that this holds for any n ≥ 3.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:244-258
    DOI: 10.1016/j.amc.2015.05.059
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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.
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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.
    2. 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.
    3. Fister, Iztok & Tepeh, Aleksandra & Fister Jr., Iztok, 2016. "Epistatic arithmetic crossover based on Cartesian graph product in ensemble differential evolution," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 181-194.

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