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Infill drilling is the first choice to increase the recovery factor, but the mission of selecting the best well location is considered a major challenge with the huge area of the reservoir and the time consumption to conducting the simulation runs that may reach hundreds to thousands. This paper adopted the design of an experiment plus a proxy optimization technique to solve this problem. Where the Latin Hypercube represents the DoE while the radial basis function network represents the artificial intelligence proxy model. The proxy model mimics the reservoir model to reduce the computation time and speed up the well-placement optimization process. The Latin Hypercube approach is used to generate data to train the proxy model to construct a reliable artificial intelligence model to predict the best wells locations. The results are very optimistic and encouraging to rely on using the art-of-state to construct a proxy model to conduct the infill wells drilling optimization. Where the increase in cumulative oil production for the optimized case is more than the un-optimized case by 6.45% and the decrease in the field cumulative water production for the optimized case is less than the un-optimized case by 16.11% from 2020 to 2040. [ABSTRACT FROM AUTHOR]

The generalized l-connectivity kl(G) of a graph G is a generalization of classical connectivity k(G) with k2(G) = k(G). It serves to measure the capability of connection for any l vertices. The folded Petersen cube network FPQn;k can be used to model the topological structure of a communication-efficient multiprocessor. This paper shows that the generalized 4-connectivity of the folded Petersen cube network FPQn;k is n + 3k - 1. As a corollary, the generalized 3-connectivity of FPQn;k also is obtained and the results on the generalized 4-connectivity of hypercube Qn and folded Petersen graph FPk can be verified. These conclusions provide a foundation for studying the generalized 4-connectivity of Cartesian product graphs. [ABSTRACT FROM AUTHOR]

The configuration of algorithms is a laborious and difficult process. Thus, it is advisable to automate this task by using appropriate automatic configuration methods. The irace method is among the most widely used in the literature. By default, irace initializes its search process via uniform sampling of algorithm configurations. Although better initialization methods exist in the literature, the mixed-variable (numerical and categorical) nature of typical parameter spaces and the presence of conditional parameters make most of the methods not applicable in practice. Here, we present an improved initialization method that overcomes these limitations by employing concepts from the design and analysis of computer experiments with branching and nested factors. Our results show that this initialization method is not only better, in some scenarios, than the uniform sampling used by the current version of irace , but also better than other initialization methods present in other automatic configuration methods. [ABSTRACT FROM AUTHOR]

Highlights • The tip-over event of a generic vertical concrete dry cask is studied with a probabilistic approach. • Metamodels are developed for the canister maximum strain and overpack maximum acceleration. • Fragility and risk analysis is performed for the selected responses. • Effect of aging and variation of design parameters on the fragilities is explored. Abstract Vertical concrete dry casks, which provide an interim solution for the storage of spent nuclear fuel, are vulnerable to tip-over due to lateral loads. This paper explores the probabilistic structural response of a representative dry cask subjected to tip-over impact loads and aging effects. Considering concrete and soil material properties, thickness of the pad, angular velocity at the onset of tip-over, and age of the cask as variables, 200 configurations of the tip-over problem are generated by Latin Hypercube Sampling. To consider aging and the associated temporal variations, material properties of the steel parts vary in the generated configurations due to temperature variations. The generated tip-over scenarios are analyzed by numerical models developed and validated in a commercial finite element analysis program. Machine learning algorithms such as polynomial response surface models, multivariate adaptive regression splines, regression trees, support vector machines, Gaussian processes and neural networks are trained on datasets provided by the finite element analysis to develop metamodels for the maximum strain of the canister and maximum acceleration of the concrete overpack. These metamodels offer statistical approximating functions that enable efficient impact fragility analysis and evaluation of the sensitivity of the fragility to age, concrete material properties of the cask and pad, and pad thickness. The effect of aging due to alkali-silica reaction on the strain fragility is also studied, and recommendations regarding the design of vertical concrete dry casks are provided. Risk analysis is performed to estimate the dry storage cask's risk of failure (i.e., probability of limit state exceedance) and to uncover the effect of age and design parameters on the probability of strain and acceleration exceeding predefined limits. The risk analysis shows that the probability of canister failure in the tip-over event is negligible. That is, despite expected cracks in the concrete overpack, the structural integrity of the dry cask system subjected to the tip-over impact loads is retained. [ABSTRACT FROM AUTHOR]

Abstract In this work we present VCube-PS , a topic-based Publish/Subscribe system built on the top of a virtual hypercube-like topology. Membership information and published messages are broadcast to subscribers (members) of a topic group over dynamically built spanning trees rooted at the publisher. For a given topic, the delivery of published messages respects the causal order. VCube-PS was implemented on the PeerSim simulator, and experiments are reported including a comparison with the traditional Publish/Subscribe approach that employs a single rooted static spanning-tree for message distribution. Results confirm the efficiency of VCube-PS in terms of scalability, latency, number and size of messages. Highlights • VCube-PS presents logarithmic behavior in terms of latency. • One tree per publisher instead of one per topic distributes better the load. • Messages have a small delivery delay and carry a causal barrier of reasonable size. • In a real world scenario, VCube-PS performs better than a well-known approach. • Dynamics of subscriptions temporarily induces a few false-positive messages. [ABSTRACT FROM AUTHOR]

Graph embedding is an important technology in simulating parallel structures and designing VLSI layout. Hypercube is one of the most significant interconnection networks in parallel computing systems. The exchanged hypercube is an important variant of the hypercube, which is obtained by systematically deleting edges from a hypercube. It not only retains several valuable and desirable properties of the hypercube, but also has lower hardware cost. In this paper, we first give an exact formula of minimum wirelength of exchanged hypercube layout into a grid. Furthermore, we propose an O(N) algorithm for embedding exchanged hypercube into a gird with load 1, expansion 1 and minimum wirelength and derive a linear layout of exchanged hypercube with minimum number of tracks and efficient layout areas. Finally, we present simulation experiments of our embedding algorithm on network overhead and total wirelength, which conduce to estimate the total wirelength and chip area. [ABSTRACT FROM AUTHOR]

Let S ⊆ V (G) and κ G (S) denote the maximum number r of edge-disjoint trees T 1, T 2, ..., T r in G such that V (T i) ∩ V (T j) = S for any i, j ∈ { 1, 2, ..., r } and i ≠ j ⁠. For an integer k with 2 ≤ k ≤ n ⁠, the generalized k-connectivity of a graph G is defined as κ k (G) = min { κ G (S) | S ⊆ V (G) and | S | = k } ⁠. The generalized k -connectivity is a generalization of traditional connectivity. In this paper, we focus on the Cayley graph generated by complete graphs and the Cayley graph generated by wheel graphs, denoted by C T n and W G n ⁠, respectively. We study the generalized 3-connectivity of the two kinds of graphs and show that κ 3 (C T n) = n (n − 1) 2 − 1 and κ 3 (W G n) = 2 n − 3 for n ≥ 3 ⁠. [ABSTRACT FROM AUTHOR]

A folded hypercube is obtained by adding complementary links to a hypercube. The diameter of the folded hypercube is almost half of that of the hypercube, while its degree is larger than the degree of the hypercube by only one. In this paper, we propose a stochastic link-fault-tolerant routing algorithm in a folded hypercube by introducing a limited global information called routing probabilities. For an n-dimensional folded hypercube, we have proved that the routing probabilities for all distances can be calculated in O(n2logn) time at each node and the message can be forwarded to its neighbor node at each node in O(n) time. We also conducted a computer experiment, the results of which show that our algorithm achieves a better performance than the best algorithm for a hypercube. [ABSTRACT FROM AUTHOR]

In this paper, we study the connectivity properties of the random subgraph of the n-cube generated by the k-out model and denoted by Qn(k). Let k be an integer, 1 ≤ k ≤ n-1. We let Qn(k) be the graph that is generated by independently including for every ν ∊ V(Qn) a set of k distinct edges chosen uniformly from all the (k n) sets of distinct edges that are incident to ν. We study the connectivity properties of Qn(k) as k varies. We show that without high probability (w.h.p.), Qn(1) does not contain a giant component i.e., a component that spans Ω(2n) vertices. Thereafter, we show that such a component emerges when k=2. In addition, the giant component spans all but o(2n) vertices, and hence it is unique. We then establish the connectivity threshold found at k0=log2 n-2log2log2 n. The threshold is sharp in the sense that Qn([k0]) is disconnected but Qn([k0]+1) is connected w.h.p. Furthermore, we show that w.h.p., Qn(k) is k-connected for every k≥ [k0]+1. [ABSTRACT FROM AUTHOR]

In this paper, we present and apply an approximate hypercube queuing method to analyze an emergency maintenance system within the agricultural stage of Brazil’s sugarcane industry. We incorporate differentiated service rates in the approximate hypercube method to deal with significant travel times as well as partial backup and priority in queue to mimic the dispatch policies of the system. We then applied this method using data from a case study conducted in an existing sugar and alcohol mill. We also investigated an alternative scenario for this system, as proposed by the company‘s managers, whereby the number of servers increases. The results showed that the method is an efficient way to investigate the original configuration as well as an alternative scenario for the case study. Furthermore, the method might be useful in larger applications and/or similar agro-industries. [ABSTRACT FROM AUTHOR]

The transmission system together with power management will simultaneously affect the fuel economy of the plug-in hybrid electric vehicle (PHEV) with automated mechanical transmission (AMT). This paper strives to make three contributions to realize systematic design and optimization of the transmission and power management. Firstly, a design of experiment method is proposed to redesign the current transmission system of the PHEV with Optimal Latin Hypercube Design algorithm. Then, a co-optimization method is proposed to insight into the preferable speed ratios of the redesigned transmission system with multi-island genetic and dynamic programming algorithms. Finally, a Pontryagin’s Minimum Principle-based self-identification controller is proposed to realize adaptive power management control, based on a significant finding that the constant solution of the co-state from off-line iteration optimization can be approximately identified by the mean value of the co-state with time-moving in the self-identification controller. Results demonstrate that the current 6-speed ratio AMT can be reduced to 4, the fuel economy of the redesigned transmission system can be improved by 2.9% compared to the current transmission system and the self-identification controller can further improve the fuel economy of the PHEV compared to the conventional PI controller. [ABSTRACT FROM AUTHOR]

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$. It gives a more refined quantitative analysis of indicators of the robustness of a multiprocessor system in the presence of failing links. The n processors. In this paper, the h$ -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) algorithm is designed to totally determine the exact values and $\lambda _h$ -optimality of $\lambda _h(FQ_n)$ for each $h\leq N/2$. [ABSTRACT FROM PUBLISHER]

Let G be a graph and T be a certain connected subgraph of G . The T -structure connectivity κ ( G ; T ) (resp. T -substructure connectivity κ s ( G ; T ) ) of G is the minimum number of a set of subgraphs F = { T 1 , T 2 , . . . , T m } (resp. F = { T 1 ′ , T 2 ′ , . . . , T m ′ } ) such that T i is isomorphic to T (resp. T i ′ is a connected subgraph of T ) for every 1 ≤ i ≤ m , and F 's removal will disconnect G . Let Q n and F Q n denote the n -dimensional hypercube and folded hypercube, respectively. In [12] , the κ ( Q n ; T ) and κ s ( Q n ; T ) were determined for T ∈ { K 1 , 1 , K 1 , 2 , K 1 , 3 , C 4 } . In this paper, we generalize the above results by determining κ ( Q n ; T ) and κ s ( Q n ; T ) for T ∈ { P k , C 2 k , K 1 , 4 } where 3 ≤ k ≤ n . We also determine κ ( F Q n ; T ) and κ s ( F Q n ; T ) for T ∈ { P k , C 2 k , K 1 , 3 } where n ≥ 7 and 2 ≤ k ≤ n . [ABSTRACT FROM AUTHOR]

Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras' conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∊ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5. [ABSTRACT FROM AUTHOR]

In metamodeling, the choice of sampling points is crucial for the quality of the model. In this context, the maximin Latin hypercube designs (LHD), with their spacefilling and noncollapsing properties, are particularly efficient. To this day, there is no polynomial time algorithm that produces optimal maximin LHDs, i.e., in which the minimum distance between two points (the separation distance) is maximal.We are interested in LHDs with a separation distance as large as possible. The algorithm we propose, IES, gives an approximate solution to the LHD problem regardless of its dimension and size with a theoretical performance guarantee. We introduce two upper bounds for the separation distance to find its approximation ratio. Its performance is compared with the best metaheuristic algorithm known for this problem, an appropriate simulated annealing scheme. Our algorithm defeats the metaheuristic algorithm for large instances of the problem while having a very short running time. [ABSTRACT FROM AUTHOR]

Networks play an important role in electrical and electronic engineering. It depends on what area of electrical and electronic engineering, for example there is a lot more abstract mathematics in communication theory and signal processing and networking etc. Networks involve nodes communicating with each other. Graph theory has found a considerable use in this area of research. A topological index is a real number associated with chemical constitution purporting for correlation of chemical networks with various physical properties, chemical reactivity. The concept of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index and Zagreb polynomials was established in chemical graph theory based on vertex degrees. In this paper, we extend this study to interconnection networks and derive analytical closed results of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index, Zagreb polynomials and redefined Zagreb indices for block shift network (BSN - 1) and (BSN - 2), hierarchical hypercube (HHC - 1) and (HHC - 2). [ABSTRACT FROM AUTHOR]

Diagnosability of a multiprocessor system is one important study topic, which plays an important role in measuring of the reliability of multiprocessor systems. In the work of Zhang et al. in 2016, they proposed a new measure for fault diagnosis of systems, namely, g -extra conditional diagnosability. It is defined as the diagnosability of a multiprocessor system under the assumption that every fault-free component contains more than g vertices, which can measure the reliability of interconnection networks in heterogeneous environments more accurately than traditional diagnosability. As two kind of favorable topology structures of interconnection networks, the n -dimensional hypercubes Q n and folded hypercubes F Q n have many good properties. In this paper, we investigate their g -extra conditional diagnosability and show that (a) the g -extra conditional diagnosability of Q n is ( g + 1 ) n − g − C g 2 for n ≥ 5 and 1 ≤ g ≤ n − 1 4 under the MM* model; (b) the g -extra conditional diagnosability of F Q n is ( g + 1 ) n − C g 2 + 1 for n ≥ 9 and 1 ≤ g ≤ n 4 under the MM* model. [ABSTRACT FROM AUTHOR]

Fault tolerance of an ( n , k ) -star network is measured by its h -super connectivity κ s ( h ) or h -super edge-connectivity λ s ( h ) . Li et al. (2014) [8] , (2012) [6] determined κ s ( h ) and λ s ( h ) for 0 ≤ h ≤ n − k . This paper determines that κ s ( h ) = λ s ( h ) = ( h + 1 ) ! ( n − h − 1 ) ( n − k ) ! for n − k ≤ h ≤ n − 2 . [ABSTRACT FROM AUTHOR]

Spatiotemporally representative Elementary Sampling Units (ESUs) are required for capturing the temporal variations in surface spatial heterogeneity through field measurements. Since inaccessibility often coexists with heterogeneity, a cost-efficient sampling design is mandatory. We proposed a sampling strategy to generate spatiotemporally representative and cost-efficient ESUs based on the conditioned Latin hypercube sampling scheme. The proposed strategy was constrained by multi-temporal Normalized Difference Vegetation Index (NDVI) imagery, and the ESUs were limited within a sampling feasible region established based on accessibility criteria. A novel criterion based on the Overlapping Area (OA) between the NDVI frequency distribution histogram from the sampled ESUs and that from the entire study area was used to assess the sampling efficiency. A case study in Wanglang National Nature Reserve in China showed that the proposed strategy improves the spatiotemporally representativeness of sampling (mean annual OA = 74.7%) compared to the single-temporally constrained (OA = 68.7%) and the random sampling (OA = 63.1%) strategies. The introduction of the feasible region constraint significantly reduces in-situ labour-intensive characterization necessities at expenses of about 9% loss in the spatiotemporal representativeness of the sampling. Our study will support the validation activities in Wanglang experimental site providing a benchmark for locating the nodes of automatic observation systems (e.g., LAINet) which need a spatially distributed and temporally fixed sampling design. [ABSTRACT FROM AUTHOR]

Optimal Experiment Design (OED) is a well-developed concept for regression problems that are linear-in-the-parameters. In case of experiment design to identify nonlinear Takagi-Sugeno (TS) models, non-model-based approaches or OED restricted to the local model parameters (assuming the partitioning to be given) have been proposed. In this article, a Fisher Information Matrix (FIM) based OED method is proposed that considers local model and partition parameters. Due to the nonlinear model, the FIM depends on the model parameters that are subject of the subsequent identification. To resolve this paradoxical situation, at first a model-free space filling design (such as Latin Hypercube Sampling) is carried out. The collected data permits making design decisions such as determining the number of local models and identifying the parameters of an initial TS model. This initial TS model permits a FIM-based OED, such that data is collected which is optimal for a TS model. The estimates of this first stage will in general not be ideal. To become robust against parameter mismatch, a sequential optimal design is applied. In this work the focus is on D-optimal designs. The proposed method is demonstrated for three nonlinear regression problems: an industrial axial compressor and two test functions. [ABSTRACT FROM AUTHOR]

This paper presents a fault-tolerant routing methodology for both injured hypercube and cube-connected cycles interconnection topologies. The proposed routing methodology efficiently tolerates any pattern of faulty regions with any number of faulty nodes in the network which is based on the best-first search and backtracking strategy. Deadlock freedom of the proposed routing methodology is obtained by only one virtual channel per physical channel. In order to evaluate the proposed routing methodology, a 7-dimensional hypercube network is simulated in various conditions, i.e., different traffic rates, different number of faulty nodes and different message lengths. Simulation results confirm that the proposed routing methodology in comparison with the previous methods provides acceptable performance while it significantly increases the reliability of the network. It also guarantees delivery of messages between any pair of source and destination while the network is connected. [ABSTRACT FROM AUTHOR]

An extended 1 -perfect trade is a pair ( T 0 , T 1 ) of two disjoint binary distance- 4 even-weight codes such that the set of words at distance 1 from T 0 coincides with the set of words at distance 1 from T 1 . Such trade is called primary if any pair of proper subsets of T 0 and T 1 is not a trade. Using a computer-aided approach, we classify nonequivalent primary extended 1 -perfect trades of length 10 , constant-weight extended 1 -perfect trades of length 12 , and Steiner trades derived from them. In particular, all Steiner trades with parameters ( 5 , 6 , 12 ) are classified. [ABSTRACT FROM AUTHOR]

Given a connected graph G and a non-negative integer g , the g-extra connectivity κ g ( G ) of G is the minimum cardinality of a set of vertices in G , if it exists, whose deletion disconnects G and leaves each remaining component with more than g vertices. This paper focuses on the g -extra connectivity of hypercube-like networks (HL-networks for short). All the known results suggest the equality κ g ( X n ) = f n ( g ) holds, where X n is an n -dimensional HL-network, f n ( g ) = n ( g + 1 ) − g ( g + 3 ) 2 , n ≥ 5 and 0 ≤ g ≤ n − 3 . However, in this paper, we show that this equality does not hold in general. We also prove that κ g ( X n ) ≥ f n ( g ) holds for n ≥ 5 and 0 ≤ g ≤ n − 3 . This enables us to give a sufficient condition for the equality κ g ( X n ) = f n ( g ) , which is then used to determine the g -extra connectivity of HL-networks for some small g or the g -extra connectivity of some particular subfamily of HL-networks. [ABSTRACT FROM AUTHOR]

This paper presents a novel application of hypercube framework of ant colony optimization to the virtual machine (VM) placement problem, with the objective of minimizing the power consumption and resource wastage. The aim of the VM placement is to develop an optimal placement strategy to allocate the VM's to physical servers such that the usage of physical resource is minimized. The hypercube framework of ACO differs from its usual ACO implementation in the hyperspace for the pheromone values. In other words, in the hypercube framework, the updating of pheromone values is constrained to lie between 0 to1. This constrained pheromone updating has an advantage of automatically handling the scaling of objective function values and further leads to robust version pf ACO procedure. Here, we experimentally investigate the influence of hypercube framework of ACO for virtual machine placement using three ACO variants, namely, Ant system, Max-Min Ant System, and Ant colony system. [ABSTRACT FROM AUTHOR]

Distributed Hash Tables (DHT) proved to be scalable decentralized systems providing efficient resource location. This paper concentrates on efficiency and resilience to node failures of DHT systems and presents a novel model of a distributed hash table based on a hierarchical hypercube geometry, called HyCube. The DHT geometry, the choice of the metric defining logical distances between nodes, and the routing algorithm have fundamental influence on routing efficiency and resilience. The use of the one-dimensional model (placing the nodes logically on a ring) allows the nodes to maintain sets of references called sequential neighbors - certain numbers of neighbors that are the closest existing nodes in both directions on the ring. Such a model yields a very high level of resilience to node failures. The new approach, presented in the paper, employs a variable multi-dimensional metric adopting the Steinhaus transform. Routing, lookup and search algorithms are discussed, as well as routing table nodes selection and self-organization techniques. It is shown that the new approach allows reaching a higher level of resilience to node failures, as well as a shorter average routing path length than with the use of the sequential neighbors sets. [ABSTRACT FROM AUTHOR]

The balanced hypercube network, which is a novel interconnection network for parallel computation and data processing, is a newly-invented variant of the hypercube. The particular feature of the balanced hypercube is that each processor has its own backup processor and they are connected to the same neighbors. A Hamiltonian bipartite graph with bipartition V0 ∪ V1 is Hamiltonian laceable if there exists a path between any two vertices x ∈ V0 and y ∈ V1. It is known that each edge is on a Hamiltonian cycle of the balanced hypercube. In this paper, we prove that, for an arbitrary edge e in the balanced hypercube, there exists a Hamiltonian path between any two vertices x and y in different partite sets passing through e with e ≠ xy. This result improves some known results. [ABSTRACT FROM AUTHOR]

In engineering, it is often desirable to find a subset of the set of feasible designs, a solution space, rather than a single solution. A feasible design is defined as a design which does not violate any constraints and has a performance value below a desired threshold. Performance measure, threshold value and constraints depend on the specific problem. For evaluation of a design with respect to feasibility, a model is required which maps the design parameters from the input space onto the performance measures in the output space. In state-of-the-art methodology, iterative sampling is used to generate an estimate of the frontier between feasible and infeasible regions in the input space. By evaluating each sample point with respect to feasibility, areas which contain a large fraction of feasible designs are identified and subsequently resampled. The largest hypercube containing only feasible designs is sought, because this results in independent intervals for each design parameter. Estimating this hypercube with sufficient precision may require a large number of model evaluations, depending on the dimensionality of the input space. In this paper, a novel approach is proposed for modeling the inequality constraints and an objective function in a way for which a linear formulation can be used, independently of the dimensionality of the problem. Thereby the exact solution for the largest feasible hypercube can be calculated at much lower cost than with stochastic sampling as described above, as the problem is reduced to solving a linear system of equations. The method is applied to structural design with respect to the US-NCAP frontal impact. The obtained solution is compared to numerical solutions of an identical system, which are computed using reduced order models and stochastic methods. By this example, the high potential of the new direct method for solution space computation is shown. [ABSTRACT FROM AUTHOR]

ABSTRACT We give two results for multicommodity flows in the d-dimensional hypercube [ABSTRACT FROM AUTHOR]

Fault tolerance is the ability such that a multiprocessor system operates properly in the event of the failure of some of its components. Latifi et al. [IEEE Trans. Comput. 43 (2) (1994) 218-222] proposed the notion of Rg-connectivity (κg) of a network modeled by graph G such that at least kg vertices in G should be deleted to disconnect the network, and the minimum degree of every connected component is at least g. This paper establishes κg (CCN (n)) = (n - g + 1)2g (1 ≤ g ≤ n - 2) for n-dimensional complete cubic network CCN (n). Fault diagnosability is another important metric for evaluating network reliability and availability. In 2012, Peng et al. [Appl. Math. Comput. 218 (21) (2012) 10406-10412] proposed a novel g-good-neighbor (conditional) diagnosability, which tacitly assumes that every fault-free vertex has at least g fault-free neighbors. In view of kg (CCN (n)), we show that the g-good-neighbor diagnosability of the complete cubic network CCN(n) under the PMC model (1 ≤ g ≤ n - 2) and the MM* model (1 ≤ g ≤ n - 2 and n ≥ 4) is (n - g + 2)2g - 1, respectively. [ABSTRACT FROM AUTHOR]

Node-disjoint paths have played an important role in the study of routing, reliability, and fault tolerance of an interconnection network. In this paper, we give a necessary and sufficient condition, which can be verified in O ( m n 1.5 ) time, for the existence of m node-disjoint shortest paths from one source node to other m (not necessarily distinct) target nodes, respectively, in an n -dimensional folded hypercube, where m ≤ n + 1 . Moreover, when the condition holds, the m node-disjoint shortest paths can be constructed in optimal O ( mn ) time. In the situation that all of the source node and target nodes are mutually distinct, brute-force computations show that the probability of existence of the m node-disjoint shortest paths in an n -dimensional folded hypercube is not less than 100%, 86%, 86%, 92%, and 94% for ( n , m ) = ( 3 , 4 ) , ( 4 , 4 ) , ( 5 , 6 ) , ( 6 , 6 ) , and (7, 8), respectively. [ABSTRACT FROM AUTHOR]

An efficient interconnection topology called Eisenstein–Jacobi (EJ) network has been proposed in Martínez et al. (2008). In this paper this concept is generalized to higher dimensions. Important properties such as distance distribution and the decomposition of higher dimensional EJ networks into edge-disjoint Hamiltonian cycles are explored in this paper. In addition, an optimal shortest path routing algorithm and a one-to-all broadcast algorithm for higher dimensional EJ networks are given. Further, we give comparisons between higher EJ networks and Generalized Hypercube (GHC) networks and we show that higher EJ networks cost less and have more nodes than GHC networks. [ABSTRACT FROM AUTHOR]

This paper addresses the general problem of reducing unnecessary message transmission thereby lowering overall bandwidth utilization in a Peer-to-Peer (P2P) network. In particular, we exploit the characteristics of a P2P network engineered to resemble a hypercube. The reason for doing this is to achieve constant computation time for inter-node distances that are needed in the process of query optimization. To realize such a hypercube-like engineered structure, we develop a new labeling scheme which assigns identifiers (labels) to each node and then uses these labels to determine inter-node distances as is done in a hypercube, thus eliminating the need to send out queries to find the distance from one node to another. The labels allow for creating a virtual overlay which resembles a hypercube. We prove that the labeling scheme does in fact allow for reducing bandwidth utilization in the network. To confirm our theoretical findings we conduct various experiments with randomly selected P2P networks of various sizes. Detailed statistics on the outcome of these experiments are provided which show clearly the practical utility of the labeling approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

Intended for computer experiments with both qualitative and quantitative factors, marginally coupled designs were introduced by Deng, Hung and Lin (2015) as a more economical strategy than the original, sliced space-filling designs. Among the designs constructed in Deng, Hung and Lin (2015), the corresponding designs for quantitative factors possess only the one-dimensional space-filling property with respect to each level of any factor in designs for qualitative factors. In addition, their designs for quantitative factors have clustered points. To avoid clustered points and enhance two- and higher-dimensional space-filling property in designs for quantitative factors, we propose three approaches to construct marginally coupled designs. Theoretical results of marginally coupled designs are also derived. [ABSTRACT FROM AUTHOR]

The l -wide-diameter of a graph G is the minimum integer d for which there exist at least l internally disjoint paths of length at most d between any two distinct vertices in G . This parameter measures the fault tolerance and transmission delay in communication networks modelled by graphs. Hypercube-like graphs are widely used as graph models for interconnection networks. In this paper, we study the wide-diameters of a special type of hypercube-like graphs: the Z -cubes Z n , k . It is known that Z n , k have diameter at most ⌈ n k + 1 ⌉ + 2 k in Zhu (2015). We show that the k -wide-diameter of Z n , k is at most ⌈ n k + 1 ⌉ + 2 k + k + 4 . In particular, if k = ⌈ log 2 n − 2 log 2 log 2 n ⌉ , then the k -wide-diameter of Z n , k is ( 1 + o ( 1 ) ) n log 2 n , which is asymptotically optimal. [ABSTRACT FROM AUTHOR]

A generalized neighborhood for d -dimensional cellular automata is introduced; it spans the range from von Neumann's to Moore's neighborhood using a parameter which represents the dimension of hypercubes connecting neighboring cells. Finite hypercubes and hypertoruses are studied, and the number of neighbors on their boundary and the number of connections between cells are calculated. We come to finite constructs when practically implementing computations of cellular automata. Enumerations of cells, neighbors and connections are considered and implemented in ad-hoc software which generates a canvas of hypercube and hypertorus models in the form of a Petri net. A cell model can be replaced while the underlying canvas of connections remains the same. The generalized neighborhood is extended to include a concept of radius; the number of neighbors is calculated for infinite and finite lattices. For diamond-shaped neighborhoods, a sequence is obtained whose partial sums equal Delannoy numbers. [ABSTRACT FROM AUTHOR]

Orthogonal array-based Latin hypercubes, also called U -designs, have popularly been adopted for designing a computer experiment. The relationship between the averaged discrepancy of all U -designs generated from a given orthogonal array and the generalized wordtype pattern of the orthogonal array is established. Motivated by the relationship, we define a weighted wordtype pattern and a minimum weighted aberration criterion to compare orthogonal arrays of the same parameters. U -designs generated from an orthogonal array with less weighted aberration are shown to have low discrepancies on average. Then, an algorithm to construct uniform U -designs is proposed. It begins with a minimum weighted aberration orthogonal array and its advantage is illustrated by comparing with the threshold-accepting algorithm. [ABSTRACT FROM AUTHOR]

When fitting complex models, such as finite element or discrete event simulations, the experiment design should exhibit desirable properties of both projectivity and orthogonality. To reduce experimental effort, sequential design strategies allow experimenters to collect data only until some measure of prediction precision is reached. In this article, we present a batch sequential experiment design method that uses sliced full factorial-based Latin hypercube designs (sFFLHDs), which are an extension to the concept of sliced orthogonal array-based Latin hypercube designs (OALHDs). At all stages of the sequential design, good univariate stratification is achieved. The structure of the FFLHDs also tends to produce uniformity in higher dimensions, especially at certain stages of the design. We show that our batch sequential design approach has good sampling and fitting qualities through both empirical studies and theoretical arguments. Supplementary materials are available online. [ABSTRACT FROM PUBLISHER]

The hypercube network is one of the most popular parallel computing networks since it has a simple structure and is easy to implement. The locally twisted cube is a newly introduced variant of the hypercube which has the same number of nodes and same number of connections per node as the hypercube, but has only half the diameter and better graph embedding capability as compared to hypercube. In this paper, we show that ann-dimensional locally twisted cube is constructed by forming a matching between the nodes of two disjoint copies of an-dimensional hypercube. In addition, we embed the locally twisted cube into path with minimum layout. [ABSTRACT FROM PUBLISHER]

The ( s+ t+1)-dimensional exchanged crossed cube, denoted by ECQ(s, t), proposed by Li et al., combines the advantages of the hypercube and the crossed cube. It has been proven that ECQ(s, t) has better properties than the fundamental hypercube in the aspects of the fewer edges, lower cost factor and smaller diameter. This paper studies the embedding of cycles in ECQ(s, t). It is proved that ECQ(s, t) contains an l-cycle of every length l from 4 to 2 s+ t+1 except that ECQ(2, 3) and ECQ(3, 3) do not contain a cycle of length 9 where and . This result reveals the fact that ECQ(s, t) nearly remains the cycle embedding capability, while it only has about half edges of crossed cube. [ABSTRACT FROM AUTHOR]

The strong diagnosability and conditional diagnosability are both novel concepts for measuring the reliability and fault tolerance of multicomputers. The optical multi-mesh hypercube (OMMH) networks, which integrate satisfactory features of both hypercubes and meshes and circumvent the lack of scalability of hypercubes and the large diameter of meshes, are promising optical interconnection topologies. For-OMMH networks, this study shows that the strong diagnosability is, and the conditional diagnosability isif either (a), or (b)and. [ABSTRACT FROM AUTHOR]

A graph G is considered conditional k -edge-fault hamiltonian-connected if, after k faulty edges are removed from G , under the assumption that each node is incident to at least three fault-free edges, a hamiltonian path exists between any two distinct nodes in the resulting graph. This paper focuses on the conditional edge-fault hamiltonian-connectivity of a wide class of interconnection networks called restricted hypercube-like networks ( RHLs ). An n -dimensional RHL ( R H L n ) is proved to be conditional ( 2 n − 7 ) -edge-fault hamiltonian-connected for n ≥ 5 . The technical theorem proposed in this paper is then applied to show that several multiprocessor systems, including n -dimensional crossed cubes, n -dimensional twisted cubes for odd n , n -dimensional locally twisted cubes, n -dimensional generalized twisted cubes, n -dimensional Möbius cubes, and recursive circulants G ( 2 n , 4 ) for odd n , are all conditional ( 2 n − 7 ) -edge-fault hamiltonian-connected. [ABSTRACT FROM AUTHOR]

The extraction and labeling of connected components in images play an important role in a wide range of fields, such as computer vision, remote sensing, medicine, biometrics, document analysis, robotics, among others. The automatic identification of relevant image regions allows for the development of intelligent systems to address complex problems for segmentation, classification and interpretation purposes. In this work, we present novel algorithms for labeling connected components that do not require any data structure on the labeling process. The algorithms are derived from other based upon independent spanning trees over the hypercube graph. Initially, the image coordinates are mapped to a binary Gray code axis, such that all pixels that are neighbors in the image are neighbors on the hypercube and each node that belongs to the hypercube represents a pixel in the image. We then use the algorithm proposed by Silva et al. (2013) to generate the log  N independent spanning trees over the image. The proposed methods for connected-component labeling are applied to a number of images to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

The optimum compatibility of search strategies in multidimensional databanks is investigated, where the optimality of some "natural" search strategies, for example, those based on some desired property values, on the one hand, and those based on similarity evaluations with respect to some individual "lead" entry, on the other hand, show different dependences on the dimension of the search in the space of the descriptors. The advantages of modifying these strategies to make them more compatible with one another in a dimension-dependent way is discussed, and a volume-constrained hypersphere - hypercube combination is explored if a switch of strategy might become desirable. [ABSTRACT FROM AUTHOR]