The hypercube serves as a high-performance interconnection network employed in various fields, including data center networks, network-on-chips, and wireless sensor networks. As the number of processing elements rapidly increases, these application fields are facing significant challenges in preserving communication efficiency with robust fault-tolerant mechanisms. Paths and cycles are two effective and popular tools for improving the communication efficiency of large-scale networks. Fault-tolerant path/cycle embedding is recognized as a solution to maintain communication efficiency and fault tolerance simultaneously. In this paper, we aim to enhance the fault-tolerant path/cycle embedding capability of hypercube networks by an emerging fault model, namely thePartitionedEdgeFault (PEF) model. Under this model, we put forward four distinct fault-tolerant path/cycle embedding algorithms that can handle large-scale faulty edges. Moreover, by proving the upper bound of these algorithms’ fault tolerance, we derive the optimal fault-tolerant Hamiltonian laceability and bipancyclicity of hypercubes under the PEF model. Furthermore, we conduct both theoretical and experimental analyses to show our algorithms’ outstanding fault-tolerant capability compared to the state-of-the-art. To validate the practical applicability of our theoretical results, we also develop a deadlock-free routing strategy leveraging the proposed embedding algorithm and compare its performance with benchmark routing algorithms.

Thek-aryn-cubeQknis a widely employed interconnection network for data center networks (DCNs) due to its favorable properties, including node/edge symmetry, recursive structure, regularity, and ease of deployment. Among the numerous structures studied inQkn, the cycle is fundamental for addressing various graph-related problems in DCNs. This has motivated extensive research on fault-tolerant cycle embedding withinQkn. However, existing methods for cycle embedding often exhibit limited fault tolerance since they fail to account for the dimension-oriented nature of edge faults inQkn. In this paper, we overcome this limitation by using the partitioned edge fault (PEF) model, a recently developed model that explicitly considers dimension-specific fault distributions. Under the PEF model, we propose a new indicator called partition-edge fault-tolerant bipancyclicity, which accurately reflects the practical fault characteristics ofQkn. ForQknwith even k ≥ 4, we determine the exact value of this indicator and prove its optimality under the PEF model. Moreover, forQknwith odd k ≥ 3, we develop three fault-tolerant embedding algorithms that establish a lower bound for this indicator. Furthermore, we conduct numerical evaluations and simulation experiments to analyze the bipancyclicity ofQknunder varying scales of edge faults.

The Hamiltonian path serves as a robust tool for unicast or multicast communication in parallel and distributed systems. Embedding this path structure into large-scale systems, especially those with numerous failures, remains a formidable and pressing challenge. The arrangement graph is a topology that not only generalizes many renowned network architectures but is also a promising framework for future computer systems. Extensive research has been conducted on the fault-tolerant embedding of Hamiltonian paths in the arrangement graph or its subclasses, yet these efforts have not attained the desired fault tolerance levels. In this article, we focus on significantly improving the edge fault-tolerant embedding capabilities of arrangement graphs by adopting a novel fault model, termed the partitioned edge fault model. We first prove the existence of Hamiltonian path avoiding large-scale edge faults in arrangement graphs. Then we develop a corresponding Hamiltonian path embedding algorithm with high fault-tolerant capability for arrangement graphs. Both theoretical comparisons and experimental analyses reveal that our methods yield significant enhancements in fault tolerance over existing studies. Furthermore, building upon the generated Hamiltonian path, we devise a dual-path multicast routing strategy and evaluate its latency performance.

Modern large-scale computing systems always demand better connectivity indicators for reliability evaluation. However, as more processing units have been rapidly incorporated into emerging computing systems, existing indicators (e.g.,$\ell$-component edge connectivity and$\ell$-extra edge connectivity) have gradually failed to provide the required fault tolerance. In addition, these indicators require, for example, that the faulty network should have at least$\ell$components (or that each component should have at least$\ell$nodes). These fault assumptions are not flexible enough to deal with diversified structural demands in practice circumstances. In order to address these challenges simultaneously, this article proposes two novel indicators for network reliability by utilizing the partition matroid technique, named matroidal connectivity and conditional matroidal connectivity. We first investigate the accurate values of (conditional) matroidal connectivity of$k$-ary$n$-cube$Q_{n}^{k}$, which is an appealing option as the underlying topology for modern parallel computing systems. Moreover, we propose an$O(k^{n-1})$algorithm for determining structural features of minimum edge sets whose cardinality is the conditional matroidal connectivity of$Q_{n}^{k}$. Simulation results are presented to verify our algorithm's correctness and further investigate the distribution pattern of edge sets subject to the restriction of partition matroid. We also present comparative analyses illustrating the superior edge fault tolerance of our findings in relation to prior research, which even exhibits an exponential enhancement when$k\geq 4$.

The balanced hypercube B H n plays an essential role in large-scale parallel and distributed computing systems. With the increasing probability of edge faults in large-scale networks and the widespread applications of Hamiltonian paths and cycles, it is especially essential to study the fault tolerance of networks in the presence of Hamiltonian paths and cycles. However, existing researches on edge faults ignore that it is almost impossible for all faulty edges to be concentrated in a certain dimension. Thus, the fault tolerance performance of interconnection networks is severely underestimated. This paper focuses on three measures, t -partition-edge fault-tolerant Hamiltonian, t -partition-edge fault-tolerant Hamiltonian laceable, and t -partition-edge fault-tolerant strongly Hamiltonian laceable, and utilizes these measures to explore the existence of Hamiltonian paths and cycles in balanced hypercubes with exponentially faulty edges. We show that the B H n is 2 n − 1 -partition-edge fault-tolerant Hamiltonian laceable, 2 n − 1 -partition-edge fault-tolerant Hamiltonian, and ( 2 n − 1 − 1 ) -partition-edge fault-tolerant strongly Hamiltonian laceable for n ≥ 2 . Comparison results show the partitioned fault model can provide the exponential fault tolerance as the value of the dimension n grows.

The$k$-ary$n$-cube$Q_{n}^{k}$is one of the most popular interconnection networks engaged as the underlying topology of data center networks, on-chip networks, and parallel and distributed systems. Due to the increasing probability of faulty edges in large-scale networks and extensive applications of the Hamiltonian path, it becomes more and more critical to investigate the fault tolerability of interconnection networks when embedding the Hamiltonian path. However, since the existing edge fault models in the current literature only focus on the entire status of faulty edges while ignoring the important information in the edge dimensions, their fault tolerability is narrowed to a minimal scope. This article first proposes the concept of the partitioned fault model to achieve an exponential scale of fault tolerance. Based on this model, we put forward two novel indicators for the bipartite networks (including$Q^{k}_{n}$with even$k$), named partition-edge fault-tolerant Hamiltonian laceability and partition-edge fault-tolerant hyper-Hamiltonian laceability. Then, we exploit these metrics to explore the existence of Hamiltonian paths and unpaired 2-disjoint path cover in$k$-ary$n$-cubes with large-scale faulty edges. Moreover, we prove that all these results are optimal in the sense that the number of edge faults tolerated has attended to the best upper bound. Our approach is the first time that can still embed a Hamiltonian path and an unpaired 2-disjoint path cover into the$k$-ary$n$-cube even if the faulty edges grow exponentially.

The$k$-ary$n$-cube$Q_{n}^{k}$is one of the most important interconnection networks for building network-on-chips, data center networks, and parallel computing systems owing to its desirable properties. Since edge faults grow rapidly and the path structure plays a vital role in large-scale networks for parallel computing, fault-tolerant path embedding and its related problems have attracted extensive attention in the literature. However, the existing path embedding approaches usually only focus on the theoretical proofs and produce an$n$-related linear fault tolerance since they are based on the traditional fault model, which allows all faults to be adjacent to the same node. In this paper, we design an efficient fault-tolerant Hamiltonian path embedding algorithm for enhancing the fault-tolerant capacity of$k$-ary$n$-cubes. To facilitate the algorithm, we first introduce a new conditional fault model, named Partitioned Edge Fault model (PEF model). Based on this model, for the$k$-ary$n$-cube$Q_{n}^{k}$with$n\geq 2$and odd$k\geq 3$, we explore the existence of a Hamiltonian path in$Q_{n}^{k}$with large-scale edge faults. Then we give an$O(N)$algorithm, named HP-PEF, to embed the Hamiltonian path into$Q_{n}^{k}$under the PEF model, where$N$is the number of nodes in$Q_{n}^{k}$. The performance analysis of HP-PEF shows the average path length of adjacent node pairs in the Hamiltonian path constructed by HP-PEF. We also make comparisons to show that our result of edge fault tolerance has exponentially improved other known results. We further experimentally show that HP-PEF can support the dynamic degradation of average success rate of constructing Hamiltonian paths when increasing faulty edges exceed the fault tolerance.

Imbuing robots with personality has been shown to be an effective design approach in HRI, promoting user trust and acceptance. We explore personality design in a non-anthropomorphic voice-assisted home robot. Our design approach developed three distinct robot personas: Butler, Buddy, and Sidekick, intended to differ in proactivity and emotional impact. Persona differences were signaled to users by a combination of humanoid (speech, intonation), and indirect cues (colors and movement). We use Big Five personality theory to evaluate perceived differences between personas in an exploratory Wizard of Oz study. Participants were largely able to recognize underlying personality traits expressed through these cue combinations in ways that were consistent with our design goals. The proactive Buddy persona was judged as more Extravert than the more passive Sidekick persona, and the Butler persona was perceived as more Conscientious and less Neurotic than either Buddy or Butler personas. Users also had clear preferences between different personas; they wanted robots that mimicked but accentuated their own personality. Results suggest that future designs might exploit abstract cues to signal personality traits.

In the cloud computing environment with massive information services and decision-making resources, the accuracy and reliability of information are more important than previous single closed systems. Therefore, ensuring the reliability of information and the stable operation of the system are the core problems in the research fields such as the Internet Plus and the Internet of Things. The connectivity and diagnosability are two important measures for the fault tolerance of multiprocessor systems. The g -good-neighbor conditional connectivity ( Rg -connectivity) is the minimum number of nodes that make the graph disconnected, and each node has at least g neighbors in every remaining component. The g -good-neighbor conditional diagnosability ( g -GNCD) is the maximum number of faulty processors that has been correctly identified in a system, and any fault-free processor has no less than g fault-free neighbors. Exchanged X -cubes are a class of irregular networks, obtained by deleting links from hypercubes and some variant networks of hypercubes ( X -cubes). They not only combine the advantages of X -cubes but also reduce the interconnection complexity. Exchanged X -cubes classify its nodes into two different classes clusters with a unique connecting rule. In this paper, we propose the generalized exchanged X -cubes framework so that architecture can be constructed by different connecting rules. Furthermore, we study the Rg -connectivity and g -GNCD of generalized exchanged X -cubes under the PMC and MM ∗ models. As applications, the Rg -connectivity and g -GNCD of generalized exchanged hypercubes, dual-cube-like networks, generalized exchanged crossed cubes, and locally generalized exchanged twisted cubes are determined, respectively.