Construction independent spanning trees on locally twisted cubes in parallel

Yu-Huei Chang, Jinn-Shyong Yang (), Sun-Yuan Hsieh (), Jou-Ming Chang () and Yue-Li Wang ()
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Yu-Huei Chang: National Taiwan University of Science and Technology
Jinn-Shyong Yang: National Taipei University of Business
Sun-Yuan Hsieh: National Cheng Kung University
Jou-Ming Chang: National Taipei University of Business
Yue-Li Wang: National Taiwan University of Science and Technology

Journal of Combinatorial Optimization, 2017, vol. 33, issue 3, No 10, 956-967

Abstract: Abstract Let $$LTQ_n$$ L T Q n be the n-dimensional locally twisted cube. Hsieh and Tu (Theor Comput Sci 410(8–10):926–932, 2009) proposed an algorithm to construct n edge-disjoint spanning trees rooted at a particular vertex 0 in $$LTQ_n$$ L T Q n . Later on, Lin et al. (Inf Process Lett 110(10):414–419, 2010) proved that Hsieh and Tu’s spanning trees are indeed independent spanning trees (ISTs for short), i.e., all spanning trees are rooted at the same vertex r and for any other vertex $$v(\ne r)$$ v ( ≠ r ) , the paths from v to r in any two trees are internally vertex-disjoint. Shortly afterwards, Liu et al. (Theor Comput Sci 412(22):2237–2252, 2011) pointed out that $$LTQ_n$$ L T Q n fails to be vertex-transitive for $$n\geqslant 4$$ n ⩾ 4 and proposed an algorithm for constructing n ISTs rooted at an arbitrary vertex in $$LTQ_n$$ L T Q n . Although this algorithm can simultaneously construct n ISTs, it is hard to be parallelized for the construction of each spanning tree. In this paper, from a modification of Hsieh and Tu’s algorithm, we present a fully parallelized scheme to construct n ISTs rooted at an arbitrary vertex in $$LTQ_n$$ L T Q n in $${\mathcal O}(n)$$ O ( n ) time using $$2^n$$ 2 n vertices of $$LTQ_n$$ L T Q n as processors.

Keywords: Edge-disjoint spanning trees; Independent spanning trees; Interconnection networks; Locally twisted cubes; Parallel algorithms (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0018-8

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