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Let = { T 1 , T 2 , ... , T k } be a set of k ≥ 2 spanning trees in a graph G. The k spanning trees are called completely independent spanning trees (CISTs for short) if the paths joining every pair of vertices x and y in any two trees have neither vertex nor edge in common except for x and y. Particularly, is called a dual-CIST provided k = 2. For data transmission applications in reliable networks, the existence of a dual-CIST can provide a configuration of fault-tolerant routing called protection routing. This paper investigates the problem of constructing a dual-CIST in the n -dimensional hierarchical folded cubic network H F Q n . The network is a two-level network using folded hypercube F Q n as clusters to reduce the diameter, hardware overhead and improve the fault tolerance ability. We propose a recursive algorithm to construct a dual-CIST of H F Q n in (2 2 n) time for n ≥ 2 , where the time required is the same scale as the number of vertices of H F Q n . Also, the diameter of each constructed CIST is 4 n + 1. [ABSTRACT FROM AUTHOR]

Fault detection and localization are vital for ensuring the stability of data center networks (DCNs). Specifically, adaptive fault diagnosis is deemed a fundamental technology in achieving the fault tolerance of systems. The highly scalable data center network (HSDC) is a promising structure of server-centric DCNs, as it exhibits the capacity for incremental scalability, coupled with the assurance of low cost and energy consumption, low diameter, and high bisection width. In this paper, we first determine that both the connectivity and diagnosability of the m-dimensional complete HSDC, denoted by H S D C m (m) , are m. Further, we propose an efficient adaptive fault diagnosis algorithm to diagnose an H S D C m (m) within three test rounds, and at most N + 4 m (m − 2) tests with m ≥ 3 (resp. at most nine tests with m = 2 ), where N = m · 2 m is the total number of nodes in H S D C m (m) . Our experimental outcomes demonstrate that this diagnosis scheme of HSDC can achieve complete diagnosis and significantly reduce the number of required tests. [ABSTRACT FROM AUTHOR]

"Linearly many faults" is a phenomenon observed by Cheng and Lipták in which a specific structure emerges when a graph is disconnected and often occurs in various interconnection networks. This phenomenon means that if a certain number of vertices or edges are deleted from a graph, the remaining part either stays connected or breaks into one large component along with smaller components with just a few vertices. This phenomenon can be observed in many types of graphs and has important implications for network analysis and optimization. In this paper, we first validate the phenomenon of linearly many faults for surviving graph of a burnt pancake graph B P n when removing any edge subset with a size of approximately six times λ (B P n) . For graph G, the ℓ-component edge connectivity denoted as λ ℓ (G) (resp., the ℓ-extra edge connectivity denoted as λ (ℓ) (G) ) is the cardinality of a minimum edge subset S such that G − S is disconnected and has at least ℓ components (resp., each component of G − S has at least ℓ + 1 vertices). Both λ ℓ (G) and e λ (ℓ) (G) are essential metrics for network reliability assessment. Specifically, from the property of "linearly many faults", we may further prove that λ 5 (B P n) = λ (3) (B P n) + 3 = 4 n − 3 for n ⩾ 5 ; λ 6 (B P n) = λ (4) (B P n) + 4 = 5 n − 4 and λ 7 (B P n) = λ (5) (B P n) + 5 = 6 n − 5 for n ⩾ 6 . [ABSTRACT FROM AUTHOR]

Traditional model compression techniques are dependent on handcrafted features and require domain experts, with a tradeoff between model size, speed, and accuracy. This study proposes a new approach toward resolving model compression problems. Our approach combines reinforcement-learning-based automated pruning and knowledge distillation to improve the pruning of unimportant network layers and the efficiency of the compression process. We introduce a new state quantity that controls the size of the reward and an attention mechanism that reinforces useful features and attenuates useless features to enhance the effects of other features. The experimental results show that the proposed model is superior to other advanced pruning methods in terms of the computation time and accuracy on CIFAR-100 and ImageNet dataset, where the accuracy is approximately 3% higher than that of similar methods with shorter computation times. [ABSTRACT FROM AUTHOR]

The design of interconnection networks is a fundamental aspect of high-performance computing (HPC) systems. Among the available topologies, the Galaxyfly network stands out as a low-diameter and flexible-radix network for HPC applications. Given the paramount importance of collective communication in HPC performance, in this paper, we present two different all-to-all broadcast algorithms for the Galaxyfly network, which adhere to the supernode-first rule and the router-first rule, respectively. Our performance evaluation validates their effectiveness and shows that the first algorithm has a higher degree of utilization of network channels, and that the second algorithm can significantly reduce the average time for routers to collect packets from the supernode. [ABSTRACT FROM AUTHOR]

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 inner-vertex-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 $\min \{n,\lfloor (n+m)/2\rfloor \}$ CISTs in $L$ - $RCube(n,m,k)$ for $n+m\geqslant 4$ 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. [ABSTRACT FROM AUTHOR]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2005.04.026 Byline: Fu-Hsing Wang (a), Yue-Li Wang (b), Jou-Ming Chang (c) Keywords: Graph theory; Geodetic set; Block-cactus graphs; Forcing geodetic number Abstract: A vertex set D in graph G is called a geodetic set if all vertices of G are lying on some shortest u-v path of G, where u, v [member of] D. The geodetic number of a graph G is the minimum cardinality among all geodetic sets. A subset S of a geodetic set D is called a forcing subset of D if D is the unique geodetic set containing S. The forcing geodetic number of D is the minimum cardinality of a forcing subset of D, and the lower and the upper forcing geodetic numbers of a graph G are the minimum and the maximum forcing geodetic numbers, respectively, among all minimum geodetic sets of G. In this paper, we find out the lower and the upper forcing geodetic numbers of block-cactus graphs. Author Affiliation: (a) Department of Information Management, Chungyu Institute of Technology, Keelung, Taiwan, Republic of China (b) Department of Information Management, National Taiwan University of Science and Technology, 43, Section 4, Kee-Lung Road, Taipei, Taiwan, Republic of China (c) Department of Information Management, National Taipei College of Business, Taipei, Taiwan, Republic of China Article History: Received 14 November 2003; Accepted 11 April 2005 Article Note: (footnote) [star] This research was partially supported by National Science Council under the Grants NSC93-2416-H-011-005 and NSC93-2115-M-141-001.