Constructing dual-CISTs of pancake graphs and performance assessment of protection routings on some Cayley networks

Pai, Kung-Jui; Chang, Ruay-Shiung; Chang, Jou–Ming

doi:10.1007/s11227-020-03297-9

Cited by 15 publications

(6 citation statements)

References 40 publications

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“…Currently, this conjecture has been proved to fail by counterexamples [23], [28]. For recent research results on CISTs and their applications, the reader can refer to [24]- [27] and references quoted therein. Here, we expressly point out that the construction of multiple ISTs and CIST are two different problems.…”

Section: Introductionmentioning

confidence: 99%

The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks

et al. 2021

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Section: Introductionmentioning

confidence: 99%

The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks

et al. 2021

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“…Pancake-like graphs have been studied for sorting problems [2,3,[7][8][9][10], interconnection networks in computer science [11][12][13][14][15][16], and DNA computing models in biology [17][18][19][20][21]. Finding a graph with a small network cost is like a high-performance interconnection network and a good sorting algorithm [22].…”

Section: Introductionmentioning

confidence: 99%

Recursively Divided Pancake Graphs with a Small Network Cost

Seo

Lee

2021

Symmetry

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Graphs are often used as models to solve problems in computer science, mathematics, and biology. A pancake sorting problem is modeled using a pancake graph whose classes include burnt pancake graphs, signed permutation graphs, and restricted pancake graphs. The network cost is degree × diameter. Finding a graph with a small network cost is like finding a good sorting algorithm. We propose a novel recursively divided pancake (RDP) graph that has a smaller network cost than other pancake-like graphs. In the pancake graph Pn, the number of nodes is n!, the degree is n − 1, and the network cost is O(n2). In an RDPn, the number of nodes is n!, the degree is 2log2n − 1, and the network cost is O(n(log2n)3). Because O(n(log2n)3) < O(n2), the RDP is superior to other pancake-like graphs. In this paper, we propose an RDPn and analyze its basic topological properties. Second, we show that the RDPn is recursive and symmetric. Third, a sorting algorithm is proposed, and the degree and diameter are derived. Finally, the network cost is compared between the RDP graph and other classes of pancake graphs.

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“…However, Hasunuma [12] early proved that the problem of determining whether there exists k CISTs in a graph is NP-complete, even for k = 2 (i.e., a dual-CIST). For more researches on constructing a dual-CIST or multiple CISTs on interconnection networks, please refer to [20,[22][23][24][25][26] and references quoted therein. In particular, the works in [22][23][24][25] discussed in-depth the configuration of protection routing.…”

Section: Introductionmentioning

confidence: 99%

“…For more researches on constructing a dual-CIST or multiple CISTs on interconnection networks, please refer to [20,[22][23][24][25][26] and references quoted therein. In particular, the works in [22][23][24][25] discussed in-depth the configuration of protection routing. In contrast, to the best of our knowledge, only a few studies of CISTs are related to DCNs.…”

Section: Introductionmentioning

confidence: 99%

Transmission Failure Analysis of Multi-Protection Routing in Data Center Networks with Heterogeneous Edge-Core Servers

Li¹,

Wanling²,

Chang³

et al. 2021

Preprint

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The recently proposed RCube network is a cube-based server-centric data center network (DCN), including two types of heterogeneous servers, called core servers and edge servers. Remarkably, it takes the latter as backup servers to deal with server failures and thus achieve high availability. This paper first points out that RCube is suitable as a candidate topology of DCNs for edge computing. Three transmission types are among core and edge servers based on the demand for applications' computation and instant response. We then employ protection routing to analyze the transmission failure of RCube DCNs. Unlike traditional protection routing, which only tolerates a single link or node failure, we use the multi-protection routing scheme to improve fault-tolerance capability. To configure a protection routing in a network, according to Tapolcai's suggestion, we need to construct two completely independent spanning trees (CISTs), which are edge-disjoint and innervertex-disjoint spanning trees. It is well-known that the problem of determining whether there exists a dual-CIST (i.e., two CISTs) in a network is NP-complete. A logic graph of RCube, denoted by L-RCube(n, m, k), is a network with a recursive structure. Each basic building element consists of n core servers and m edge servers, where the order k is the number of recursions applied in the structure. In this paper, we provide algorithms to construct min{n, (n + m)/2 } CISTs in L-RCube(n, m, k) for n + m 4 and n > 1. From a combination of the multiple CISTs, we can configure the desired multi-protection routing. In our simulation, we configure up to 10 protection routings for RCube DCNs. As far as we know, in past research, there were at most three protection routings developed in other network structures. Finally, we summarize some crucial analysis viewpoints about the transmission efficiency of DCNs with heterogeneous edge-core servers from the simulation results.

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Constructing dual-CISTs of pancake graphs and performance assessment of protection routings on some Cayley networks

Cited by 15 publications

References 40 publications

The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks

The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks

Recursively Divided Pancake Graphs with a Small Network Cost

Transmission Failure Analysis of Multi-Protection Routing in Data Center Networks with Heterogeneous Edge-Core Servers

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