The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks

Yang, Yicheng; Kao, Shih-Shun; Klasing, Ralf; Hsieh, Sun Yuan; Chou, Hsin-Hung; Chang, Jou–Ming

doi:10.1109/access.2021.3049290

Cited by 10 publications

(2 citation statements)

References 40 publications

(47 reference statements)

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“…From then on, this conjecture has been confirmed only for k-connected graphs with k ≤ 4 (see [9,10,14]). Since this conjecture is still unsolved for general k-connected graphs for k ≥ 5, the follow-up research mainly focused on the study of constructing ISTs on specific interconnection networks, e.g., the construction of ISTs on some variations of hypercubes [3,20,29,30,37], torus networks [28], recursive circulant graphs [34,35], and special subclasses of Cayley networks [7,8,12,13,15,19,39]. In particular, special topics related to ISTs include the research on reducing the height of the ISTs [31,33,36] and parallel construction of ISTs [4-6, 32, 37, 38].…”

Section: Introductionmentioning

confidence: 99%

A parallel algorithm for constructing multiple independent spanning trees in bubble-sort networks

Kao

Klasing

Hung

et al. 2023

Journal of Parallel and Distributed Computing

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Section: Introductionmentioning

confidence: 99%

A parallel algorithm for constructing multiple independent spanning trees in bubble-sort networks

Kao

Klasing

Hung

et al. 2023

Journal of Parallel and Distributed Computing

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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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A Parallel Algorithm for Constructing Multiple Independent Spanning Trees in Bubble-Sort Networks

Kao

Klasing

Hung

et al. 2021

Algorithmic Aspects in Information and Management

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The use of multiple independent spanning trees (ISTs) for data broadcasting in networks provides a number of advantages, including the increase of fault-tolerance and secure message distribution. Thus, the designs of multiple ISTs on several classes of networks have been widely investigated. Kao et al. [Journal of Combinatorial Optimization 38 (2019) 972-986] proposed an algorithm to construct independent spanning trees in bubble-sort networks. The algorithm is executed in a recursive function and thus is hard to parallelize. In this paper, we focus on the problem of constructing ISTs in bubble-sort networks Bn and present a non-recursive algorithm. Our approach can be fully parallelized, i.e., every vertex can determine its parent in each spanning tree in constant time. This solves the open problem from the paper by Kao et al. Furthermore, we show that the total time complexity O(n • n!) of our algorithm is asymptotically optimal, where n is the dimension of Bn and n! is the number of vertices of the network.

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The Construction of Multiple Independent Spanning Trees on Burnt Pancake Networks

Cited by 10 publications

References 40 publications

A parallel algorithm for constructing multiple independent spanning trees in bubble-sort networks

A parallel algorithm for constructing multiple independent spanning trees in bubble-sort networks

Recursively Divided Pancake Graphs with a Small Network Cost

A Parallel Algorithm for Constructing Multiple Independent Spanning Trees in Bubble-Sort Networks

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