Parallel construction of optimal independent spanning trees on Cartesian product of complete graphs

Chen, Xie-Bin

doi:10.1016/j.ipl.2010.11.018

Cited by 7 publications

(4 citation statements)

References 25 publications

(30 reference statements)

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“…It is well-known that parts of the interconnection networks are constructed by Cartesian product of graphs, e.g., hypercubes are Cartesian product of a sequence of 2-cliques, and multidimensional torus are Cartesian product of a sequence of cycles with varied lengths. Therefore, our result generalizes the previous works [2,16,17] and [24].…”

Section: Discussionsupporting

confidence: 92%

“…Moreover, there are several results of ISTs on some special classes of graphs. Especially, the graph classes related to interconnection networks, such as product graphs [2,14], planar graph [7], chordal rings [9,21], de Bruijn and Kautz digraphs [5,6], hypercubes [16,24], locally twisted cubes [12,13], folded hyercubes [19], folded hyper-stars [20], star graphs [15], multidimensional torus [17], recursive circulant graphs [22,23], odd graphs [10] and even networks [11].…”

Section: Introductionmentioning

confidence: 99%

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Optimal Independent Spanning Trees on Cartesian Product of Hybrid Graphs

Yang

Chang

2012

The Computer Journal

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A set of k spanning trees rooted at the same vertex r in a graph G are called independent spanning trees (ISTs) if for any vertex x = r, the k paths from v to r, one path in each tree, are internally disjoint. The design of ISTs on graphs has applications to fault-tolerant broadcasting and secure message distribution in networks. It was conjectured that for any k-connected graph there exist k ISTs rooted at any vertex of the graph. The conjecture has been proved true for k-connected graphs with k 4, and remains open otherwise. In this paper, we deal with the problem of constructing ISTs on Cartesian product of a sequence of hybrid graphs including cycles and complete graphs. Consequently, this result generalizes a number of previous works.

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Section: Discussionsupporting

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Optimal Independent Spanning Trees on Cartesian Product of Hybrid Graphs

Yang

Chang

2012

The Computer Journal

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“…From then on, this conjecture has been shown to be true for k-connected graphs with k 4 (see [11,13,20,48] for k = 2, 3, 4, respectively) and is still open for k 5. Also, this conjecture has been confirmed for several restricted classes of graphs, e.g., graphs related to planarity [18,19,25,26], graphs defined by Cartesian product [6,27,29,30,34,40,44], variations of hypercubes [5,[8][9][10]24,32,33,38,49], special Cayley graphs [22,23,28,39,42,43], and chordal ring [21,41]. In particular, [5,[7][8][9][10][32][33][34]40,49] are published after 2012.…”

Section: Introductionmentioning

confidence: 79%

A fully parallelized scheme of constructing independent spanning trees on Möbius cubes

Yang

Chang

et al. 2014

J Supercomput

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A set of spanning trees in a graph is said to be independent (ISTs for short) if all the trees are rooted at the same node r and for any other node v( = r ), the paths from v to r in any two trees are node-disjoint except the two end nodes v and r . It was conjectured that for any n-connected graph there exist n ISTs rooted at an arbitrary node. Let N = 2 n be the number of nodes in the n-dimensional Möbius cube M Q n . Recently, for constructing n ISTs rooted at an arbitrary node of M Q n , Cheng et al. (Comput J 56(11):1347(Comput J 56(11): -1362(Comput J 56(11): , 2013 and (J Supercomput 65 (3):1279-1301, 2013), respectively, proposed a sequential algorithm to run in O(N log N ) time and a parallel algorithm that takes O(N ) time using log N processors. However, the former algorithm is executed in a recursive fashion and thus is hard to be parallelized. Although the latter algorithm can simultaneously construct n ISTs, it is not fully parallelized for the construction of each spanning tree. In this paper, we present a nonrecursive and fully parallelized approach to construct n ISTs rooted at an arbitrary node of M Q n in O(log N ) time using N nodes of M Q n as processors. In particular, we derive useful properties from the description of paths in ISTs, which make the proof of independency to become easier than ever before.

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“…In addition to the hypercubes mentioned earlier, there are also other graphs for which constructions of optimal ISTs have been found. Among them are cartesian products of complete graphs [28], hybrid graphs [29], even [30] and odd graphs [31].…”

Section: Adding Locality To the Picturementioning

confidence: 99%

CASA: Congestion and Stretch Aware Static Fast Rerouting

Foerster

Pignolet²,

Schmid

et al. 2019

IEEE INFOCOM 2019 - IEEE Conference on Computer Communications

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To meet the stringent requirements on the maximally tolerable disruptions of traffic under link failures, many communication networks feature some sort of static failover mechanism for fast rerouting. However, configuring such static failover mechanisms to achieve a high degree of robustness is known to be challenging, in particular when packet tagging or dynamic node state cannot be used. This paper initiates the systematic study of such local fast failover mechanisms which not only provide connectivity guarantees, even under multiple link failures, but also account for the quality of the resulting failover routes, with respect to locality (i.e., route length) and congestion. Failover quality has received less attention in the literature so far, yet it is increasingly important to support emerging applications. We first show that there exists an inherent tradeoff in terms of achievable locality and congestion of failover routes. We then present CASA, an algorithm providing a high degree of robustness as well as a provable quality of fast rerouting. CASA combines two crucial static resilient routing techniques: combinatorial designs and arc-disjoint arborescences. We complement our formal analysis with a simulation study, in which we compare our algorithms with the state-of-the-art in different scenarios and show benefits in terms of stretch, load, and resilience.

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Parallel construction of optimal independent spanning trees on Cartesian product of complete graphs

Cited by 7 publications

References 25 publications

Optimal Independent Spanning Trees on Cartesian Product of Hybrid Graphs

Optimal Independent Spanning Trees on Cartesian Product of Hybrid Graphs

A fully parallelized scheme of constructing independent spanning trees on Möbius cubes

CASA: Congestion and Stretch Aware Static Fast Rerouting

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