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A Fast Parallel Algorithm for Constructing Independent Spanning Trees on Parity Cubes

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  • Chang, Yu-Huei
  • Yang, Jinn-Shyong
  • Chang, Jou-Ming
  • Wang, Yue-Li

Abstract

Zehavi and Itai (1989) proposed the following conjecture: every k-connected graph has k independent spanning trees (ISTs for short) rooted at an arbitrary node. An n-dimensional parity cube, denoted by PQn, is a variation of hypercubes with connectivity n and has many features superior to those of hypercubes. Recently, Wang et al. (2012) confirmed the ISTs conjecture by providing an O(NlogN) algorithm to construct n ISTs rooted at an arbitrary node on PQn, where N=2n is the number of nodes in PQn. However, this algorithm is executed in a recursive fashion and thus is hard to be parallelized. In this paper, we present a non-recursive and fully parallelized approach to construct n ISTs rooted at an arbitrary node of PQn in O(logN) time using N processors. In particular, the constructing rule of spanning trees is simple and the proof of independency is easier than ever before.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:489-495
    DOI: 10.1016/j.amc.2015.06.081
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    Cited by:

    1. 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.

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