Independent spanning trees of chordal rings

Iwasaki, Yukihiro; Kajiwara, Yuka; Obokata, Koji; Igarashi, Yoshihide

doi:10.1016/s0020-0190(98)00205-1

Cited by 45 publications

(6 citation statements)

References 8 publications

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“…Independent spanning trees have been studied in several topologies, including chordal rings [14], de Bruijn and Kautz digraphs [15], [16], and product graphs [17].…”

Section: Related Workmentioning

confidence: 99%

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Moinet¹,

Darties²,

Gastineau³

et al. 2017

2017 IEEE 13th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob)

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Abstract-We investigate the problem of computing Completely Independent Spanning Trees (CIST) under a practical approach. We aim to show that despite CISTs are very challenging to exhibit in some networks, they present a real interest in ad-hoc networks and can be computed to enhance the network robustness. We propose an original ILP formulation for CISTs and we show through simulation results on representative network models that several CISTs can be computed when the network density is sufficiently high. These results tend to reinforce the interest of CISTs for various network operations such as robustness, load-balancing, traffic splitting, . . . As an important point, our results show that both the density and the number of nodes have an impact on the number of CISTs that can be found on ad-hoc networks.

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“…Independent spanning trees have been studied in several topologies, including chordal rings [14], de Bruijn and Kautz digraphs [15], [16], and product graphs [17].…”

Section: Related Workmentioning

confidence: 99%

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Moinet¹,

Darties²,

Gastineau³

et al. 2017

2017 IEEE 13th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob)

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“…Previous researches for investigating algorithmic properties of chordal rings can refer to [4], [12], [13]. In particular, Iwasaki et al [11] proposed a linear time algorithm for constructing four ISTs on a chordal ring. At a later time, Yang et al [16] make an improvement on the construction by reducing the heights of ISTs.…”

Section: Examplementioning

confidence: 99%

Completely Independent Spanning Trees on Some Interconnection Networks

Pai

Yang

Yao

et al. 2014

IEICE Trans. Inf. & Syst.

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SUMMARYLet T 1 , T 2 , . . . , T k be spanning trees in a graph G. If, for any two vertices u, v of G, the paths joining u and v on the k trees are mutually vertex-disjoint, then T 1 , T 2 , . . . , T k are called completely independent spanning trees (CISTs for short) of G. The construction of CISTs can be applied in fault-tolerant broadcasting and secure message distribution on interconnection networks. Hasunuma (2001) first introduced the concept of CISTs and conjectured that there are k CISTs in any 2k-connected graph. Unfortunately, this conjecture was disproved by Péterfalvi recently. In this note, we give a necessary condition for k-connected k-regular graphs with k/2 CISTs. Based on this condition, we provide more counterexamples for Hasunuma's conjecture. By contrast, we show that there are two CISTs in 4-regular chordal rings CR (N, d) with N = k(d − 1) + j under the condition that k 4 is even and 0 j 4. In particular, the diameter of each constructed CIST is derived.

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“…There is a number of interesting properties unique to this particular subclass. Iwasaki et al [25] have shown that for every graph in C(n; q) there are four independent spanning trees rooted at each vertex. In other words, between every pair of (source, destination) vertices there are four edge-disjoint paths, the maximum possible number for a 4-regular graph.…”

Section: Choosing the Initial Topologymentioning

confidence: 99%

Seeds for a Heterogeneous Interconnect

Hackett

Ajwani²,

Ali

et al. 2013

2013 IEEE International Symposium on Parallel &Amp; Distributed Processing, Workshops and PHD Forum

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Abstract-Traditionally, a parallel application is partitioned, mapped and then routed on a network of compute nodes where the topology of the interconnection network is known beforehand and is homogeneous. However, such homogeneity in interconnects is rarely needed for several important classes of applications. Nevertheless such interconnects are designed this way, i.e., with redundant links, to accommodate the communication patterns of a wide range of applications. However, with recent advances in technology for optical circuit switches, it is now possible to construct a network with much fewer links, and to make the link endpoints configurable to suit the communication pattern of a given application. While this is economical (saving both links and the power to run them), it raises the difficult problem of how to configure the network and how to reconfigure it quickly when the application's communication pattern changes. Since the space of all configurable topologies is large and determining the quality of a topology is a time-consuming process, it is not feasible to explore the entire space.One way of dealing with this limitation is to start the search from a "good" initial topology and then conduct a restricted search around it. The success of such a strategy crucially depends on the choice of the initial or seed topology. In the past, such an initial topology was computed by mimicking the communication requirements of the application. In this paper, we propose a different approach by showing that interconnect topologies such as chordal rings (circulant graphs) chosen based on metrics such as bisection width and average shortest path length can provide a better starting point. The topology obtained by searching around such an initial topology provides almost as good a performance as an application-specific initial topology, and the search time is significantly reduced.

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Independent spanning trees of chordal rings

Cited by 45 publications

References 8 publications

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Completely Independent Spanning Trees on Some Interconnection Networks

Seeds for a Heterogeneous Interconnect

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