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A biased assimilation model of opinion dynamics is a nonlinear model, in which opinions exchanged in a social network are multiplied by a state-dependent term having the bias as exponent and expressing the bias of the agents toward their own opinions. The aim of this article is to extend the bias assimilation model to signed social networks. We show that while for structurally balanced networks, polarization to an extreme value of the opinion domain (the unit hypercube) always occurs regardless of the value of the bias, for structurally unbalanced networks, a stable state of indecision (corresponding to the centroid of the opinion domain) also appears, at least for small values of the bias. When the bias grows and passes a critical threshold, which depends on the amount of "disorder" encoded in the signed graph, then a bifurcation occurs and opinions become again polarized. Funding Agencies|National Natural Science Foundation of China [61733018]; Australian Research Council [DP190103615]; Swedish Research Council [2020-03701]

Online Ride Hailing (ORH) services enable a rider to request a taxi via a smartphone app in real time. When using ORH services, users (including riders and taxis) have to submit their locations to the ORH server. With received locations, the ORH server makes online ride matching between riders and taxis. There are serious privacy concerns for users to reveal location information to ORH servers. In this paper, we propose an efficient and privacy-preserving ride matching scheme for ORH services, named EPRide. EPRide can find the taxi with the minimum road distance to serve an incoming rider, while protecting the location information of both taxis and riders against ORH servers or other curious servers. In EPRide, we propose an efficient exact shortest road distance computation approach over encrypted data, which converts road distance computation into Hamming distance computation over packed ciphertexts by using road network hypercube embedding and somewhat homomorphic encryption. Meanwhile, we design a secure comparison protocol, which efficiently compares encrypted distances in parallel by using ciphertexts blinding and packing, without leaking any distance. Theoretical analysis and experimental evaluations show that EPRide is secure, accurate and efficient.

Cyberspace is not a “vacuum space”, and it is normal that there are inevitable viruses and worms in cyberspace. Cyberspace security threats stem from the problem of endogenous security, which is caused by the incompleteness of theoretical system and technology of the information field itself. Thus it is impossible and unnecessary for us to build an “aseptic” cyberspace. On the contrast, we must focus on improving the “self-immunity” of network. Literally, endogenous security is an endogenous effect from its own structural factors rather than external ones. The $t/k$ t / k -diagnosis strategy plays a very important role in measuring endogenous network security without prior knowledge, which can significantly enhance the self-diagnosing capability of network. As far as we know, few research involves $t/k$ t / k -diagnosis algorithm and $t/k$ t / k -diagnosability of interconnection networks under MM* model. In this article, we propose a fast $f(r,k+1)/k$ f ( r , k + 1 ) / k -diagnosis algorithm of complexity $O(Nr^2)$ O ( N r 2 ) , say $G$ G MIS $k$ k DIAGMM*, for a general $r$ r -regular network $G$ G under MM* model by designing a 0-comparison subgraph $M_0(G)$ M 0 ( G ) , where $N$ N is the size of $G$ G . We determine that the $t/k$ t / k -diagnosability $(t(G)/k)^M$ ( t ( G ) / k ) M of $G$ G under MM* model is $f(r,k+1)$ f ( r , k + 1 ) by $G$ G MIS $k$ k DIAGMM* algorithm. Moreover, we establish the $(t(G)/k)^M$ ( t ( G ) / k ) M of some interconnection networks under MM* model, including BC networks, $(n,l)$ ( n , l ) -star graph networks, and data center network DCells. Finally, we compare $(t(G)/k)^M$ ( t ( G ) / k ) M with diagnosability, conditional diagnosability, pessimistic diagnosability, extra diagnosability, and good-neighbor diagnosability under MM* model. It can be seen that $(t(G)/k)^M$ ( t ( G ) / k ) M is greater than other fault diagnosabilities in most cases.

The $t/k$ t / k -diagnosability and $h$ h -extra connectivity are regarded as two important indicators to improve the network reliability. The $t/k$ t / k -diagnosis strategy can significantly improve the self-diagnosing capability of a network at the expense of no more than $k$ k fault-free nodes being mistakenly diagnosed as faulty. The $h$ h -extra connectivity can tremendously improve the real fault tolerability of a network by insuring that each remaining component has no fewer than $h+1$ h + 1 nodes. However, there is few result on the inherent relationship between these two indicators. In this article, we investigate the reason that caused the serious flawed results in (Liu, 2020), and we propose a diagnosis algorithm to establish the $t/k$ t / k -diagnosability for a large-scale connected network $G$ G under the PMC model by considering its $h$ h -extra connectivity. Let $\kappa _h(G)$ κ h ( G ) be the $h$ h -extra connectivity of $G$ G . Then, we can deduce that $G$ G is $\kappa _h(G)/h$ κ h ( G ) / h -diagnosable under the PMC model with some basic conditions. All $\kappa _h(G)$ κ h ( G ) faulty nodes can be correctly diagnosed in the large-scale connected network $G$ G and at most $h$ h fault-free nodes would be misdiagnosed as faulty. The complete fault tolerant method adopts combinatorial properties and linearly many fault analysis to conquer the core of our proofs. We will apply the newly found relationship to directly obtain the $\kappa _h(G)/h$ κ h ( G ) / h -diagnosability of a series of well known networks, including hypercubes, folded hypercubes, balanced hypercubes, dual-cubes, BC graphs, star graphs, Cayley graphs generated by transposition trees, bubble-sort star graphs, alternating group graphs, split-star networks, $k$ k -ary $n$ n -cubes and $(n,k)$ ( n , k ) -star graphs.

This paper proposes a reliable hypercube queuing problem where servers (e.g., vehicles) can be dispatched either individually or jointly as cooperative units, and these servers are subjected to probabilistic disruptions. The probability of a server disruption depends on the amount of resources (e.g., firefighter staffing number) allocated to this server. If any server in a cooperation unit is disrupted, a less preferred (e.g., based on capabilities and source station) but functioning and available unit will be dispatched instead. This paper derives formulas for steady-state system performance metrics for this new hypercube queuing system. The queuing model is embedded into a mixed-integer non-linear program to optimize the allocation of resources so as to minimize the total costs under server disruptions. An empirical case study is used to compare the system performance measures under a range of implementation scenarios, and sensitivity analyses are conducted to reveal insights.

Recently, studies on multidimensional seismic data interpolation through rank-constrained matrix or tensor completion have led to many effective methods, with satisfactory results. Despite the success of the rank-constrained matrix completion methods, e.g., damped rank reduction (DRR), and the rank-constrained tensor completion methods, e.g., high-order orthogonal iteration (HOOI), strong noise and highly decimated traces could still make the reconstruction results not acceptable. In this article, we find that implementing only one rank constraint to solve the multidimensional seismic data recovery problem is not sufficient. Therefore, we consider a hybrid method to reconstruct the noisy and incomplete traces based on a new mixed rank-constrained (MRC) algorithm. The proposed MRC algorithm aims to take advantage of the merits of both the rank-constrained matrix and tensor completion models to restore the missing data. We first apply the unfolding and folding operator to the 4-D spatial hypercube data. Then, for each iteration, we connect the DRR and the HOOI approaches in the same framework to solve the proposed MRC model. The proposed MRC model aims to provide an enhanced level of rank constraint to improve the signal-to-noise ratio (SNR) of the recovered data. Synthetic and field 5-D seismic data are used to compare the performance of the new method with the HOOI and DRR methods. The comparison via visual inspection and numerical analysis reveals the better performance of the proposed MRC algorithm.

Aiming to reduce the distortion in the existing reversible watermarking for 3D mesh models, this paper generalizes two-dimensional (2D) region nesting to ${n}$ -dimensional space, and proposes a general region nesting based semi-fragile reversible watermarking for authenticating 3D mesh models by combing watermark generation based on vertex projection and mesh topology. For any ${n}$ -dimensional space, each hypercube space is partitioned into several nested watermark sub-spaces, and the watermark is embedded by placing the original vertex and the mapped vertex on a straight line. The watermark is extracted by acquiring the position of the vertices, and its original coordinates can be restored by inverse mapping. Furthermore, a new coordinate system is built for 3D mesh models based on reference vertices to achieve semi-fragility, and the watermarks generated by vertex projection and mesh topology is utilized for integrity authentication. Experimental results and analysis show that the proposed scheme can significantly reduce the distortion, achieve semi-fragility in RST (Rotation, Scaling and Translation) and vertex reordering, identify the tampering type, and accomplish tampering location at vertex level. It has great potential to be applied for content authentication of 3D mesh models.

In this paper, we develop a framework for path-planning on abstractions that are not provided to the agent a priori but instead emerge as a function of the available computational resources. We show how a path-planning problem in an environment can be systematically approximated by solving a sequence of easier to solve problems on abstractions of the original space. The properties of the problem are analyzed, and a number of theoretical results are presented and discussed. A numerical example is presented to show the utility of the approach and to corroborate the theoretical findings. We conclude by providing a discussion detailing the connections of the proposed approach to anytime algorithms and bounded rationality.

The attackers in a network may have a tendency of targeting on a group of clustered nodes, and they hope to avoid the existence of significant large communication groups in the remaining network, such as botnet attack, DDoS attack, and Local Area Network Denial attack. Current various kinds of connectivity do not well reflect the fault tolerance of a network under these attacks. This observation inspires a new measure for network reliability to resist the block attack by taking into account of the dispersity of the remaining nodes. Let $G$ G be a network, $C\subset V(G)$ C ⊂ V ( G ) and $G[C]$ G [ C ] be a connected subgraph . Then $C$ C is called an $h$ h -faulty-block of $G$ G if $G-C$ G - C is disconnected, and every component of $G-C$ G - C has at least $h+1$ h + 1 nodes. The minimum cardinality over all $h$ h -faulty-blocks of $G$ G is called $h$ h -faulty-block connectivity of $G$ G , denoted by ${FB}\kappa _h(G)$ F B κ h ( G ) . In this article, we determine ${FB}\kappa _h(Q_n)$ F B κ h ( Q n ) for $n$ n -dimensional hypercube $Q_n$ Q n ( $n\geq 4$ n ≥ 4 ), a classic interconnection network. We establish that ${FB}\kappa _h(Q_n)=(h+2)n-3h-1$ F B κ h ( Q n ) = ( h + 2 ) n - 3 h - 1 for $0\leq h\leq 1$ 0 ≤ h ≤ 1 , and ${FB}\kappa _h(Q_n)=(h+2)n-4h+1$ F B κ h ( Q n ) = ( h + 2 ) n - 4 h + 1 for $2\leq h\leq n-2$ 2 ≤ h ≤ n - 2 , respectively. Larger $h$ h -faulty-block connectivity implies that an attacker will have to stage an attack to a bigger block of connected nodes, so that each remaining components will not be too small, which will in turn limit the size of large components. In other words, there will not be great disparity in sizes between any two remaining components, and hence there will less likely be a significantly large remaining communication group. The larger the $h$ h -faulty-block, the more difficult for an attacker to achieve that goal. As a consequence, the resistance of the network against the attacker will increase. Our experiments also show that as $h$ h increases, the $h$ h -faulty-block gets larger, and the size disparity between any two remaining components decreases. In turn, as expected, the size of the largest remaining communication group becomes smaller.

A network's diagnosability is the maximum number of faulty vertices that the network can discriminate solely by performing mutual tests among vertices. The original diagnosability without any condition is often rather low because it is bounded by the network's minimum degree. The $h$ -extra fault diagnosability is an important and widely accepted diagnostic strategy as a new measure of diagnosability, which guarantees that the scale of every component is at least $h+1$ in the remaining system. Moreover, it increases the allowed faulty vertices, hence enhancing the diagnosability of the network. There have been lots of state-of-the-art literatures concerning the $h$ -extra fault diagnosability. Although there are some methods to theoretically prove the extra fault diagnosability of some other well-known networks under MM* model, these methods have some serious flaws when there exists a 4-cycle in these networks. In this article, we investigate the reason that caused the flawed results in some references, and we derive a different, broadly applicable, and complete fault tolerant method to establish the extra fault diagnosability in an $n$ -dimensional alternating group graph $AG_n$ under MM* model. The complete fault tolerant method adopts combinatorial properties and linearly many fault analysis to conquer the core of our proofs. Moreover, we compare the extra fault diagnosability of $AG_n$ with various types of fault diagnosability, including the diagnosability, strong diagnosability, conditional diagnosability, $t/k$ -diagnosability, and pessimistic diagnosability. It can be seen that the extra fault diagnosability is greater than all the other types of fault diagnosability.

We consider a cache-aided interference network which consists of a library of $N$ files, $K_{T}$ transmitters and $K_{R}$ receivers (users), each equipped with a local cache of size $M_{T}$ and $M_{R}$ files respectively, and connected via a discrete-time additive white Gaussian noise (AWGN) channel. Each receiver requests an arbitrary file from the library. The objective is to design a cache placement without knowing the receivers’ requests and a communication scheme such that the sum Degrees of Freedom (sum-DoF) of the delivery is maximized. This network model with one-shot transmission was firstly investigated by Naderializadeh et al. , who proposed a scheme achieving an order-optimal one-shot sum-DoF of $\min \left \{{\frac {M_{T}K_{T}+K_{R}M_{R}}{N}, K_{R}}\right \}$ . One of the biggest limitations of this scheme is the requirement of high subpacketizations. This paper attempts to design new algorithms to reduce the file subpacketization in such a network without hurting the sum-DoF. In particular, we propose a new approach for both prefetching and linearly coded delivery based on a combinatorial design called hypercube . The proposed approach reduces the subpacketization exponentially in terms of $K_{R} M/N$ ( $M=M_{T}$ or $M_{R}$ represents the transmitter/receiver cache size) and achieves the identical one-shot sum DoF when $\frac {M_{T}K_{T}+K_{R}M_{R}}{N} \leq K_{R}$ .

To store and process big data, large-scale data centers are built to interconnect a huge number of servers, which is a challenging task due to the network scalability and performance. In this article, we study the underlying common principles behind the existing data center network architectures on dual-port servers. We find that the existing architectures hardly achieve both large scalability and bisection width simultaneously. As a result, we propose a novel fabric of switches (FoS), which is recursively constructed on the flexible division of switch ports by means of a complete graph. The novel FoS benefits data center networks by flexible design space and double-exponential scalability, as well as small diameter and large bisection width. DPCell is constructed by inserting a dual-port server between any two adjacent switches in the novel FoS, which inherits good properties of the embedded FoS. Comparison with other architectures shows DPCell can achieve both large scalability and bisection width with a small diameter. Evaluation results show that DPCell demonstrates good performance in average routing delay and average load on servers under different degrees of network traffic.

Information granules are fundamental, abstract, and easy-to-operate constructs supporting the human-centered handling way in granular computing (GrC). One of the basic properties of information granules comes with its hierarchy. Information granularity is the quantification expression of hierarchy of an information granule. Forming information granules with multigranularity to hierarchically describe the nature of data is an important task in GrC. In this article, a cone-shaped fuzzy set-based granular description method with multigranularity is proposed for multidimensional data. Its fundamental idea is to realize the synergy of quantification of information granularity and a hierarchical description of data by means of $\alpha$ –cuts of cone-shaped fuzzy sets. The proposed method first partition the entire data set into a series of data chunks. Then, some mutually nonoverlapping cone-shaped fuzzy sets are constructed by optimally determining their cores and support radii in terms of the coverage of $\alpha$ –cuts of these fuzzy sets to the data located in individual chunks and the corresponding specificity. Finally, by implementing $\alpha$ –cuts processing for these constructed cone-shaped fuzzy sets, a collection of families of hyper-spherical information granules used to hierarchically describe the structural characteristics of the data set are completely emerged. Besides, the quality of the resulting families of hyper-spherical information granules is evaluated along the granular perspective and the application perspective, respectively. A series of experimental studies concerning several synthetic and publicly available data sets are covered. The experimental results demonstrate the superiority of the proposed granular description method of data with multigranularity.

This paper addresses the relative position coordinated control problem for spacecraft formation flying under an undirected communication graph, whilst considering mass uncertainties, external disturbances, and limited communication resources. A new event-triggered information transmission mechanism is first presented, where each spacecraft only requires accessing to the states of neighbors intermittently. Subsequently, a novel event-based coordinated control scheme is proposed by combining a smooth adaptive projection rule that confines the parameter estimations to well-defined bounded convex hypercubes. Under the proposed control framework, the information exchange among spacecraft occurs only when the specified event is triggered, thereby significantly reducing the communication load and saving the onboard resources. Furthermore, a positive lower bound on interevent time intervals is guaranteed to exclude Zeno behavior. By virtue of Lyapunov stability analysis and graph theory, it is proved that the relative position tracking errors can converge to small invariant sets around the origin, and that all closed-loop signals are bounded, even in the presence of mass uncertainties and external disturbances. Finally, numerical simulations are given to evaluate the effectiveness and highlight the advantages of the developed control algorithm.

A set of spanning trees $T_1,T_2,\ldots, T_k$ T 1 , T 2 , ... , T k in a network $G$ G are Completely Independent Spanning Trees (CISTs) if for any two nodes $u$ u and $v$ v in $V(G)$ V ( G ) , the paths between $u$ u and $v$ v in any two trees have no common edges and no common internal nodes. CISTs have important applications in data center networks, such as fault-tolerant multi-node broadcasting, fault-tolerant one-to-all broadcasting, reliable broadcasting, secure message distribution, and so on. The augmented cube $AQ_n$ A Q n is a prominent variant of the well-known hypercube $Q_n$ Q n , and having the important property of scalability, and both $Q_n$ Q n and $AQ_n$ A Q n have been proposed as the underlying structure for a data center network. The data center network based on $AQ_n$ A Q n is denoted by $AQDN_n$ A Q D N n , and the logic graph of $AQDN_n$ A Q D N n is denoted by $L\text{-}AQDN_n$ L - A Q D N n . In this article, we study how to construct $n-1$ n - 1 CISTs in $L\text{-}AQDN_n$ L - A Q D N n . The constructed $n-1$ n - 1 CISTs are optimal in the sense that $n-1$ n - 1 is the maximally allowed CISTs in $L\text{-}AQDN_n$ L - A Q D N n . The correctness of our construction algorithm is proved. It is the first time a direct relationship is established between the dimension of a hypercube-family network and the number of CISTs it can host.

The coastal zone imager (CZI) onboard HY-1C satellite provides a new data source to monitor the lake environments. Here, we provided a preliminary evaluation for the applications of CZI on inland lakes and a comparison with the in situ , Landsat-8 operational land imager (OLI), and Sentinel-2 multispectral instrument (MSI) measurements. First, the in-orbit signal-to-noise ratios (SNRs) were estimated based on homogenous ocean pixels. SNRs of CZI reached ~200:1 in the visible bands and ~150:1 at the near-infrared bands, which are comparable with the OLI and slightly higher than those of the MSI. Then, the performance of 6SV and fast line-of-sight atmospheric analysis of hypercubes (FLAASH) models on the retrievals of remote sensing reflectance ( $R_{\mathrm {rs}}$ ) from CZI measurements was evaluated. 6SV-derived $R_{\mathrm {rs}}$ showed higher accuracy than that of FLAASH, validated by the synchronous in situ ( $R^{2} \simeq 0.50$ , absolute percent difference (APD) $\simeq ~20$ %) and OLI-derived $R_{\mathrm {rs}}$ ( $R^{2} \simeq ~0.75$ , APD $\simeq ~5$ %). Finally, the abilities of CZI to observe cyanobacterial bloom, suspended particular matter (SPM), and chlorophyll- $a$ (Chl $a$ ) were assessed. CZI-derived, the area of cyanobacterial bloom and SPM, showed good agreements with the results yielded by the OLI and MSI data on May 24, 2019, in Lake Taihu ( $R^{2} = 0.68$ , root-mean-square error (RMSE) = 9.68 mg/L, APD = 13.52% for SPM). While CZI only has four wide bands, Chl $a$ derived by CZI using an empirical algorithm was relatively consistent with MSI-derived values. CZI demonstrated a decent performance in monitoring the environments of large lakes, and it is expected to add the bands for atmospheric correction and further works in the small-medium lakes in the future.

Most evolutionary many-objective optimization (EMaO) algorithms start with a description of a number of the predefined set of reference points on a unit simplex. So far, most studies have used the Das and Dennis’s structured approach for generating well-spaced reference points. Due to the highly structured nature of the procedure, this method cannot produce an arbitrary number of points, which is desired in an EMaO application. Although a layer-wise implementation has been suggested, EMO researchers always felt the need for a more generic approach. Motivated by earlier studies, we introduce a metric for defining well-spaced points on a unit simplex and propose a number of viable methods for generating such a set. We compare the proposed methods on a variety of performance metrics such as hypervolume (HV), deviation in triangularized simplices, distance of the closest point pair, and variance of the geometric means to nearest neighbors in up to 15-D spaces. We show that an iterative improvement based on Riesz $s$ -energy is able to effectively find an arbitrary number of well-spaced points even in higher-dimensional spaces. Reference points created using the proposed Riesz $s$ -energy method for a number of standard combinations of objectives and reference points as well as a source code written in Python are available publicly at https://www.egr.msu.edu/coinlab/blankjul/uniform .

Fully homomorphic encryption enables to perform arbitrary computation over encrypted data, providing a powerful tool for secure outsourced computation on an untrusted environment. This paper investigates secure outsourced computation of matrix determinant based on fully homomorphic encryption. We propose an efficient secure outsourced computation scheme for matrix determinant based on an efficient matrix encoding technique called hypercube structure which packs a matrix into a single ciphertext. Experimental results show that our scheme efficiently computes the matrix determinant in the ciphertext domain. Finally, we show that our proposed scheme can be easily applied as a submodule in the high-level applications.

Designing multidimensional constellations (MdCs) is an integral part of sparse code multiple access (SCMA). Since the optimal maximum a posteriori (MAP) receiver for SCMA is too complex in most applications, one highly popular technique is the near-optimal message passing algorithm (MPA), where its performance improves with increasing the signal-to-noise ratio (SNR) and the number of iterations. When the number of MPA iterations has to be limited (e.g., low-latency and/or low-complexity and/or energy-sensitive applications), the performance gap between MAP and MPA becomes significant, especially at low-to-medium SNRs. Inspired by the promising features of hypercubes when used along with bit-interleaved coded modulation, we construct novel MdCs which are based on a unitary rotation of a hypercube by a rotation angle that aims to achieve the minimum frame-error-rate (FER). By exploiting special properties of hypercubes, we fit a second-order rational polynomial to a few measured FER samples, and find a close-to-optimal rotation angle at each SNR and MPA iteration. Our proposed MdCs provide substantial performance gains (as much as 2 dB) in comparison to the best known SCMA MdCs in the literature, especially in low-to-medium SNR regions when the number of MPA iterations has to be low, and in the presence of 5G-compliant LDPC codes.

With increasing penetration of renewable energy and active market participation, power system operation scenarios and patterns have increased exponentially. This has led to challenges in identifying a good subset of scenarios for routine planning, operation, and emerging machine learning applications. To address these challenges, we develop an approach integrating comprehensive exploratory data analyses and smart sampling techniques to identify and select a small subset of representative power system scenarios that maintain the coverage of system scenarios and operation envelope, therefore, leading to very efficient, yet representative studies and analysis. We propose a hierarchical Latin Hypercube Sampling (LHS) technique for smart sampling, which allows free-form distributions of system load and considers generator commitment status along with generation levels. A set of performance metrics are also defined for systematic evaluation of the adequacy and efficiency of the sampled cases. The developed approach and metrics are demonstrated using the Texas 2000 bus system in this paper and will be extended to the more complex real world systems such as Western Interconnect System.

We consider wireless device-to-device (D2D) caching networks with single-hop transmissions. Previous work has demonstrated that caching and coded multicasting can significantly increase per user throughput. However, the state-of-the-art coded caching schemes for D2D networks are generally impractical because content files are partitioned into an exponential number of packets with respect to the number of users if both library and memory sizes are fixed. In this paper, we present two combinatorial approaches of D2D coded caching network design with reduced packetizations and desired throughput gain compared to the conventional uncoded unicasting. The first approach uses a “hypercube” design, where each user caches a “hyperplane” in this hypercube and the intersections of “hyperplanes” represent coded multicasting codewords. In addition, we extend the hypercube approach to a decentralized design. The second approach uses the Ruzsa-Szemeredi graph to define the cache placement. Disjoint matchings on this graph represent coded multicasting codewords. Both approaches yield an exponential reduction of packetizations while providing a per-user throughput that is comparable to the state-of-the-art designs in the literature. Furthermore, we apply spatial reuse to the new D2D network designs to further reduce the required packetizations and significantly improve per user throughput for some parameter regimes.

The generalized hypercube (GH) is one key interconnection network with excellent topological properties. It contains many other interconnection topologies, such as the hypercube network, the complete graph, the mesh network, and the $k$ k -ary $n$ n -cube network. It can also be used to construct some data center networks, such as HyperX, BCube, FBFLY, and SWCube. However, the construction cost of GH is high since it contains too many links. In this paper, we propose a novel low cost interconnection architecture called the exchanged generalized hypercube (EGH). We study the properties of EGH, such as the number of edges, the degree of vertices, connectivity, diameter, and diagnosability. Then, we give a routing algorithm to find the shortest path between any two distinct vertices of EGH. Furthermore, we design an algorithm to give disjoint paths between any two distinct vertices of EGH. In addition, we propose two local diagnosis algorithms: LDT $_{EGH}$ E G H and LDWB $_{EGH}$ E G H in EGH under PMC model and MM model, respectively. Simulation results demonstrate that even if the proportion of faulty vertices in EGH is up to 25 percent, the probability that these two diagnosis algorithms can successfully determine the status of vertices is more than 90 percent. As far as the number of edges is concerned, the analysis shows that the construction cost of EGH is much less than that of GH. We could regard this work as the basis for proposing future new high performance topologies.

The grey prediction evolution algorithm based on the even grey model (GPEAe) proposed by Z.B.Hu et al. in 2019 is a competitively stochastic real-parameter optimization algorithm with characters of simple code, less parameters and strong exploration capability. To improve the algorithmic overall performance, a topological opposition-based learning strategy (TOBL) is first developed to enhance its exploitation capability in this paper. The TOBL determines offsprings by calculating the Manhattan distances between the current best individual and all the vertices of the hypercube inspired by the opposition-based learning strategy. An improved grey prediction evolutionary algorithm based on the TOBL (TOGPEAe) is then proposed. The performance of the TOGPEAe is tested on CEC2005, CEC2014 benchmark functions and a test suite composed of six engineering design problems. The experimental results of the TOGPEAe are very competitive compared with those of the original GPEAe and other state-of-the-art algorithms.

Given two regular graphs $G$ G and $H$ H such that the vertex degree of $G$ G is equal to the number of vertices in $H$ H , the compound graph $G(H)$ G ( H ) is constructed by replacing each vertex of $G$ G by a copy of $H$ H and replacing each edge of $G$ G by an additional edge connecting random vertices in two corresponding copies of $H$ H , respectively, under the constraint that each vertex in $G(H)$ G ( H ) is incident with only one additional edge, exactly. $L$ L - $HSDC_m(m)$ H S D C m ( m ) is a compound graph $G(H)$ G ( H ) , where $G$ G is a hypercube $Q_m$ Q m and $H$ H is a complete graph $K_m$ K m , which is defined by focusing on the connected relation between servers in the novel data center network $HSDC_m(m)$ H S D C m ( m ) proposed in [30]. A set of $k$ k spanning trees in a graph $G$ G are called completely independent spanning trees (CISTs for short) if the paths joining every pair of vertices $x$ x and $y$ y in any two trees have neither vertex nor edge in common, except for $x$ x and $y$ y . In this paper, we give a sufficient condition for the existence of $k$ k CISTs in a kind of compound graph. Furthermore, a specific construction algorithm is provided. As corollaries of the main results, the existences of two CISTs for $m\geq 4$ m ≥ 4 ; three CISTs for $m\geq 8$ m ≥ 8 and four CISTs for $m\geq 10$ m ≥ 10 in $L$ L - $HSDC_m(m)$ H S D C m ( m ) are gotten directly.

As an extension of the n-dimensional hypercube Qn, the n-dimensional folded hypercube denoted as FQn, which can be structured from Qn adding an edge to every pair of vertices with complementary addresses.FQn possesses many properties superior to those of Qn, such as diameter, fault diameter, connectivity, and so on. In this paper, let FFe denote the set of faulty edges in FQn and assume that each vertex is incident to at least three fault-free edges in FQn - FFe. Then, we show that FQn - FFe contains a fault-free Hamiltonian cycle of length 2n, where n ≥ 3 and |FFe| ≤ 3n - 7.

The optical transpose interconnection system (OTIS) network has many application in architecture for parallel as well as in distributed network. The optical translate interconnection system utilizes a straightforward pair of lenslet clusters to execute a coordinated interconnection that is valuable for mix based multistage interconnection networks, work of-trees network processors, and hypercubes. In Cancan (2019) and Hayat et al. (2014), different interconnection network has studied related to topological indices. In this article we have computed the Ve-degree and Ev-degree base topological indices of swapped network by taking path and complete graph as original graphs. We have included some dedicated formulas for different types of topological indices for the OTIS swapped network by taking the path and complete graph on $n$ vertices as basis of graph.

A significant indicator used in evaluating the reliability of a multiprocessor system is fault diagnosability. Researchers concentrate on the diagnosability of the entire system while ignoring important local information about the system. In our paper, an innovative concept of fault diagnosability, called $g$ -good-neighbor local diagnosability, is put forward to study the diagnosability of a system at a node under the $g$ -good-neighbor condition. Moreover, we obtain the relationship between the local diagnosability of a system at each node and the whole system’s diagnosability under the $g$ -good-neighbor condition. Under the PMC model, we prove that the $g$ -good-neighbor local diagnosability of an $n$ -dimensional hypercube network $Q_{n}$ at each node is at least $2^{g} (n-g+1)-1$ for $0 \leq g \leq n-3$ and that when $n-2 \leq g \leq n-1$ , the $g$ -good-neighbor local diagnosability of $Q_{n}$ at each node is $2^{n-1}-1$ . Further, we easily derive the diagnosability of hypercube $Q_{n}$ under the $g$ -good-neighbor condition.

Conventional sub-trajectory clustering is used to identify similarities among multiple trajectories. Existing methods tend to overlook many of the relevant sub-trajectories; others require a road network as input; all are significantly slowed down considerably by large datasets. In this paper, we propose a novel approach to clustering sub-trajectory in which trajectories are transformed into a set of Hypercubes. The Hypercubes are pairwise-matched to find an intersection and then clustered accordingly. The performance of the proposed scheme was compared with that of grid clustering (i.e., constant time technique) in terms of memory usage, computational speed, and compared with a state-of-art method, TraClus, by assessing their accuracy. The experiment results show that Hypercube clustering can identify common sub-trajectories more swiftly and with less memory usage than grid clustering. The accuracy of Hypercube clustering is superior to TraClus.

Shape complexity is a hard-to-quantify quality, mainly due to its relative nature. Biased by Euclidean thinking, circles are commonly considered as the simplest. However, their constructions as digital images are only approximations to the ideal form. Consequently, complexity orders computed in reference to circle are unstable. Unlike circles which lose their circleness in digital images, squares retain their qualities. Hence, we consider squares (hypercubes in $\mathbb Z^{n}$ ) to be the simplest shapes relative to which complexity orders are constructed. Using the connection between $L^\infty $ norm and squares we effectively encode squareness-adapted simplification through which we obtain multi-scale complexity measure, where scale determines the level of interest to the boundary. The emergent scale above which the effect of a boundary feature (appendage) disappears is related to the ratio of the contacting width of the appendage to that of the main body. We discuss what zero complexity implies in terms of information repetition and constructibility and what kind of shapes in addition to squares have zero complexity.

The $h$ h - extra node-connectivity of a graph $G$ G is the size of a minimal node-set, whose removal will disconnect $G$ G , but each remaining component has no fewer $h+1$ h + 1 nodes. Based on $h$ h -extra node-connectivity, the $h$ h - extra conditional fault-diagnosability of networks has been proposed for a better, more realistic measure of networks’ fault-tolerability. It is the maximal $x$ x such that $G$ G is $h$ h -extra conditionally $x$ x -fault-diagnosable. This paper will establish a relationship between the $h$ h -extra node-connectivity and $h$ h -extra conditional fault-diagnosability for a regular graph $G$ G , under the classic PMC diagnostic model. We will apply the newly found relationship to a variety of well-known regular networks, to directly obtain their $h$ h -extra conditional fault-diagnosability. The significance of the paper's work is that it relates the notions of $h$ h -extra node-connectivity and $h$ h -extra conditional fault-diagnosability, so that a regular network's $h$ h -extra conditional fault-diagnosability may be known once its $h$ h -extra node-connectivity is known.

In this paper, we investigate the distributed constrained containment control problem for continuous-time multiagent systems with nonconvex control input constraints. A nonlinear projection containment control algorithm for followers with double-integrator continuous-time dynamics is proposed. We show that each follower finally stays in the convex hull formed by multiple stationary leaders, provided that for each follower, there exists at least one directed path from leaders to it in the union of the graphs in each bounded time interval. Finally, a simulation example is implemented to illustrate theoretical results.

Diversity preservation plays an important role in the design of multi-objective evolutionary algorithms, but the diversity performance assessment of these algorithms remains challenging. To address this issue, this paper proposes a performance metric and a multi-objective test suite for the diversity assessment of multiobjective evolutionary algorithms. The proposed metric assesses both the evenness and spread of a solution set by projecting it to a lower-dimensional hypercube and calculating the "volume" of the projected solution set. The proposed test suite contains eight benchmark problems, which pose stiff challenges for existing algorithms to obtain a diverse solution set. Experimental studies demonstrate that the proposed metric can assess the diversity of a solution set more precisely than existing ones, and the proposed test suite can be used to effectively distinguish between algorithms with respect to their diversity performance.

Ji et al. (IEEE Transactions on Information Theory, 62(2): 849–869, 2016) first studied coded caching in device-to-device (D2D) networks, and proposed a D2D coded caching scheme, which is referred to as the JCM scheme. In practice, we prefer to design a scheme with its two important targets, i.e., the rate (the maximal total amount of transmission) and packet number ${F}$ , as small as possible. In this paper, we first propose a simple array called D2D placement delivery array (DPDA) to characterize the placement phase and the delivery phase in D2D networks. Consequently, some D2D coded caching schemes can be realized by an appropriate DPDA. Second, a lower bound on the rate of a DPDA is derived. And, we show that the JCM scheme achieves our lower bound. However, it is well known that its packet number ${F}$ increases exponentially with the number of users ${K}$ . So, we propose two classes of new schemes by constructing DPDAs. One reduces the packet number exponentially with K compared with the JCM scheme while keeping the rate near to our lower bound. The other further reduces ${F}$ to increasing sub-exponentially with ${K}$ .

As the volume of data keeps growing rapidly, more and more storage devices, servers and network devices are continuously added into data centers to store, manage and analyze the data. The industry experience indicates that, instead of a huge number of servers added at a time, the data center network also expands gradually by adding a small number of servers from time to time. As a result, how to achieve an incremental scalability is becoming a very important challenge in designing modern data center network architectures in order to maintain the topological properties unchanged when the size of data centers grows. In this paper, we propose a new type of data center network architecture named HSDC (High Scalability Data Center Network Architecture) based on the hypercube network. The HSDC is constructed by using $m$m-port switches and 2-port servers. The fault-tolerant routing algorithm designed in this paper for HSDC can be executed on any vertex and is able to construct a path between any pair of vertices. In order to achieve an incremental scalability, we further propose three types of incomplete HSDC structures that allow gradually adding servers into the structures, while maintaining all the topological properties. The simulation experiments and performance results demonstrate that the throughput of HSDC is comparable to that of Fat-Tree, BCube and DCell. Furthermore, the analysis results indicate that HSDC strikes a good balance among diameter, bisection width, incremental scalability, cost and energy consumption in contrast to the state-of-the-art data center network architectures.

The g-good neighbor connectivity κg(G) and g-good-neighbor diagnosability tg(G) are two important parameters to evaluate the reliability and fault tolerance for an interconnection network G. So far, almost all known results about κg(G) and tg(G) are about special g except the hypercubes, the star graphs, the k-ary n-cubes, and so on. In this paper, we focus on κg(HHCn) and tg(HHCn) for the n-dimensional hierarchical hypercube network HHCn for 1 ≤ g ≤ m - 1 and m ≥ 2, where n = 2m + m. We show that κg(HHCn) = 2g(m + 1 - g) for 1 ≤ g ≤ m - 1. In addition, we show that tg(HHCn) = 2g(m + 2 - g) - 1 under the PMC model and MM* model for 1 ≤ g ≤ m - 1.

The Estimated Time of Arrival (ETA) that predict the travel time of a given GPS trajectory has been extensively used in route planning. Deep learning has been widely applied to ETA prediction. However, prediction tasks involve some challenges, such as small data size, low GPU’s precision, high training loss, and low accuracy. Herein, we present a new machine-learning algorithm called HyperETA for ETA prediction. HyperETA is based on a extraordinary clustering method, called Hypercube Clustering. We conducted experiments to compare HyperETA with a deep-learning-based method called DeepTTE by using taxi trajectories as a benchmark. Two variations of both methods were evaluated. The results indicated that HyperETA outperformed the deep-learning approach in terms of prediction accuracy.

A network's diagnosability is the maximum number of faulty vertices the network can discriminate solely by performing mutual tests among the vertices. It is an important measure of a network's robustness. The original diagnosability without any condition is often rather low because it is bounded by the network's minimum degree. Several conditional diagnosability have been proposed in the past to increase the allowed faulty vertices, and hence enhancing the diagnosability of the network. The g-good-neighbor conditional diagnosability is the maximum number of faulty vertices a network can guarantee to identify, under the condition that every fault-free vertex has at least g fault-free neighbors (i.e., good neighbors). In this paper, we establish the g-good-neighbor conditional diagnosability for the (n; k)-arrangement graph network A n;k . We will show that, under both the PMC model and the comparison model, the A n;k 's g-good-neighbor conditional diagnosability is [(g + 1)k - g](n - k), which can be several times higher than the A n;k 's original diagnosability.

Reliability analysis of an interconnection network is of great significance to the design and maintenance of multiprocessor systems. The $h$ -extra edge-connectivity of a given interconnected network $G$ with $N$ processors, denoted by $\lambda _h(G)$ , is the minimum cardinality of set of faulty links, such that whose removal will disconnect the network with all its resulting components having at least $h$ processors for $h\leq N/2$ . It gives a more refined quantitative analysis of indicators of the robustness of a multiprocessor system in the presence of failing links. The $n$ -dimensional folded hypercube $FQ_n$ , as one of potential interconnected networks, is a well-known variation of the hypercube structure with $N=2^{n}$ processors. In this paper, the $h$ -extra edge-connectivity of the network $FQ_n$ , $\lambda _h(FQ_n)$ , is first investigated for each well-defined positive integer $h\leq N/2$ . We divide the interval $1\leq h\leq N/2$ into some subintervals and obtain some properties of $\lambda _h(FQ_n)$ in these subintervals. Then, we deduce a recursive relation of $\lambda _h(FQ_n)$ . Based on this recursion, an efficient $O({\log}_2(N))$ algorithm is designed to totally determine the exact values and $\lambda _h$ -optimality of $\lambda _h(FQ_n)$ for each $h\leq N/2$ .

Assume that there are at most $t$ faulty vertices. A system is conditionally ( $t,k$ )- diagnosable if at least $k$ faulty vertices (or all faulty vertices if fewer than $k$ faulty vertices remain) can be identified in each iteration under the assumption that every vertex is adjacent to at least one fault-free vertex. Let $\kappa _c(G)$ be the conditional vertex connectivity of $G$ , which measures the vertex connectivity of $G$ according to the assumption that every vertex is adjacent to at least one fault-free vertex. Let $\Delta (G)$ be the maximum degrees of the given graph $G$ . When a graph $G$ satisfies the condition that for any pair of vertices with distance two has at least two common neighbors in $G$ , we show the following two results: 1) An $r$ -regular network $G$ containing $N$ vertices is conditionally $\left(\frac{N+\sqrt{\frac{4\kappa (G)N}{(r+1)(r-1)}}-2}{r+1},\kappa _c(G)\right)$ -diagnosable, where $r \geq 3$ and $N \geq \frac{(r+1)(25r-9)}{4\kappa (G)}$ . 2) An irregular network $G$ containing $N$ vertices is conditionally $(\frac{N}{\Delta (G)+1}-1,\kappa _c(G))$ -diagnosable. By applying the above results to multiprocessor systems, we can measure conditional $(t,k)$ -diagnosabilities for augmented cubes, folded hypercubes, balanced hypercubes, and exchanged hypercubes.

Fault diagnosis has played a major role in measuring the reliability of multiprocessor systems. The diagnosability of many well-known multiprocessor systems has been widely investigated. Conditional diagnosability is a novel property of measuring diagnosability by adding a further condition that any fault set cannot contain all the neighbors of every node in the system. Several known structural properties of $(n,k)$ -star graphs are exhibited. Based on these properties, we investigate the conditional diagnosability of $(n,k)$ -star graphs under the PMC model, and show that it is 1) $\left\lceil \frac{n}{2}\right\rceil -1$ for $n\geq 4$ and $k=1$ , and 2) $n+3k-6$ for $2\leq k\leq n-3$ .

Compared with accurate diagnosis, the system's self-diagnosing capability can be greatly increased through the t/k-diagnosis strategy at most k vertexes to be mistakenly identified as faulty under the comparison model, where k is typically a small number. Based on the Preparata, Metze, and Chien (PMC) model, the n-dimensional hypercube network is proved to be t/k-diagnosable. In this paper, based on the Maeng and Malek (MM)* model, a novel t/k-fault diagnosis (1 ≤ k ≤ 4) algorithm of n-dimensional hypercube, called t/k-MM*-DIAG, is proposed to isolate all faulty processors within the set of nodes, among which the number of fault-free nodes identified wrongly as faulty is at most k. The time complexity in our algorithm is only O(2 n n 2 ).

This paper proposed a probabilistic load flow analysis of correlated wind farms based on Copula theory. This method addresses the linear and non-linear dependence between random variables more efficiently and accurately than other methods. The proposed method is nearly unconstrained to the marginal probability distribution types of the input random variables. The dependency between the input random variables is established using Copula theory in this paper. An improved Latin hypercube sampling is adopted due to the real discrete data. Uncertainty and dependence factors are considered to access the load flow of the power system accurately and comprehensively. The validity of the probability distribution between the correlated random variables is evaluated by adopting the power output of wind farms located in New Jersey. The effectiveness and accuracy of the proposed model are investigated using the comparative test in modified IEEE 14-bus and IEEE 118-bus test systems.

Exchanged hypercube $EH(s,t)$ is a typical hypercube variant, which is built up by systematically removing a range of edges from hypercube $Q_{s+t+1}$ . $EH(s,t)$ preserves several advantages of hypercube and has better properties in terms of diameter and cost. Diagnosability and conditional diagnosability have been two important measures of self-diagnostic capability. Normally, conditional diagnosability is several times higher than its diagnosability because conditional diagnosability neglects the occurrence of low probability. In this paper, we study the properties of $EH(s,t)$ and present some elementary topological and connectivity theorems. Then, based on the above results, we determine its conditional diagnosability under the MM* model.

Bijective connection (BC) networks, including a family of interconnection networks of multiprocessor systems, have been studied extensively due to its desirable properties, such as lower diameter, high reliability, and diagnosability. To meet the demand of processing integrating tasks with large-scale and complex architectures, it is significant to explore alternative interconnection networks for multiprocessor configuration. To this end, we propose a novel framework called hyper bijective connection network (HBC network) as an extension of BC networks, which allows to study the properties of other potential interconnection networks in unity rather than in individual. We prove that when $n\geq 3, m\geq 2$ , every $n$ -dimensional HBC network $H_{n}(m)$ has (edge) connectivity $m+n-2$ , super connectivity $2n+m-4$ , and super edge-connectivity $2n+2m-6$ , and is super-connected and super-edge-connected. These results indicate the high reliability of HBC networks. Moreover, we analyze three classic diagnosabilities of a HBC network, including $t_{p}$ -, $t_{1}/t_{1}$ -, and $t/k$ - diagnosability. We show that when $n\geq 3$ and $m\geq 2$ , an $n$ -dimensional HBC network $H_{n}(m)$ is $(m+n-2)$ -diagnosable, $(2n+m-4)/ (2n+m-4)$ -diagnosable, and $t(m,n,k)/~k$ -diagnosable, where $0\leq k \leq m+n-2$ and $t(m,n,k)=(k+1)n+(m-2)- ({(k+1)(k+2)}/{2})+1$ . Besides, it is shown that the corresponding properties for BC networks can be derived naturally as special cases of that for HBC networks.

Latin hypercube designs are frequently used in estimating the mean output value of computer simulations given random environmental factors. Sliced Latin hypercube designs are designs that can be partitioned into a number of batches so that both the whole design and the batches achieve optimal univariate uniformity. Such designs are useful for computer simulations that are carried out in batches, come from multiple resources, or have categorical variables. All existing sliced Latin hypercube designs have equal batch sizes. In this paper, we propose a new type of sliced Latin hypercube design that has unequal batch sizes and show their advantages theoretically and numerically.

The design space exploration (DSE) has become a major challenge in microprocessors design due to the increasing complexity of microprocessor architecture and the extremely time-consuming software simulation technology. To more effectively and efficiently perform DSE, recently machine learning techniques are widely explored to build predictive models with a small set of simulations. However, most previous models are supervised models and the training samples are randomly selected. Thus they still suffered from high simulation cost or low prediction accuracy. In order to minimize the simulation overhead for DSE, this paper proposes an efficient DSE method which combines Latin hypercube sampling and semi-supervised ensemble learning technique. Latin hypercube sampling is first employed to select a small set of representative design points for simulation. Then a semi-supervised learning based AdaBoost model (SemiBoost) is proposed to predict the responses of the configurations that have not been simulated. We conduct extensive evaluations on the benchmarks of SPEC CPU2006 suite, and the experimental results demonstrate that the proposed SemiBoost model is superior to existing state-of-the-art models in terms of both efficiency and effectiveness.

The twisted hypercube-like networks (THLNs) include some well-known hypercube variants. A graph $G$ is $k$ -fault-tolerant Hamiltonian connected if $G-F$ remains Hamiltonian connected for every $F\subset V(G)\cup E(G)$ with $|F|\leq k$ . This paper is concerned with the fault-tolerant Hamiltonian connectivity of an $n$ -dimensional ( $n$ -D) THLN. Let $G_{n}$ be an $n$ -D THLN ( $n\geq 5$ ) and $F$ be a subset of $V(G_{n})\cup E(G_{n})$ with $|F|\leq n-2$ . We show that for arbitrary vertex-pair $(u,v)$ in $G_{n}-F$ , there exists a $(n-2)$ -fault-tolerant Hamiltonian path joining vertices $u$ and $v$ except $(u,v)$ being a weak vertex-pair in $G_{n}-F$ . The technical theorem proposed in this paper can be applied to several multiprocessor systems, including $n$ -D crossed cubes $CQ_{n}$ , $n$ -D twisted cubes $TQ_{n}$ for odd $n$ , $n$ -D locally twisted cubes $LTQ_{n}$ , and $n$ -D Mobius cubes $MQ_{n}$ .

Diagnosability is an important parameter for evaluating the reliability of multiprocessor systems. $t/t$ -diagnosability and $t/k$ -diagnosability are both new indexes for measuring the reliability of a system. An $n$ -dimensional augmented cube network ( $AQ_{n}$ ) is a variant of an $n$ -dimensional hypercube network. In this paper, we first prove that an $n$ -dimensional augmented cube network is $(4n-8)/ (4n-8)$ -diagnosable, which implies that the $t/t$ -diagnosability of $AQ_{n}$ is approximately two times larger than its classical $t$ -diagnosability. Some useful properties of $AQ_{n}$ not reported by previous studies are proposed. By employing these new properties, we prove that $AQ_{n}$ is $t/k$ -diagnosable, which implies that the $t/k$ -diagnosability is approximately $(k+1)$ times larger than $2n-1$ , i.e., the $t$ -diagnosability of $AQ_{n}$ , where $t=2(k+1)n-(({3(k+1)(k+2)})/{2})+1$ , $k\leqslant ({4n}/{9})-({13}/{9})$ , and $n> 5$ .

Over the past decade, many data centers have been constructed around the world due to the explosive growth of data volume and type. The cost and energy consumption have become the most important challenges of building those data centers. Data centers today use commodity computers and switches instead of high-end servers and interconnections for cost-effectiveness. In this paper, we propose a new type of interconnection networks called Exchanged Cube-Connected Cycles (ExCCC) . The ExCCC network is an extension of Exchanged Hypercube (EH) network by replacing each node with a cycle. The EH network is based on link removal from a Hypercube network, which makes the EH network more cost-effective as it scales up. After analyzing the topological properties of ExCCC , we employ commodity switches to construct a new class of data center network models, namely ExCCC-DCN , by leveraging the advantages of the ExCCC architecture. The analysis and experimental results demonstrate that the proposed ExCCC-DCN models significantly outperform four state-of-the-art data center network models in terms of the total cost, power consumption, scalability, and other static characteristics. It achieves the goals of low cost, low energy consumption, high network throughput, and high scalability simultaneously.