We study embeddings of the n-dimensional hypercube into the circuit with 2nvertices.We prove that the circular wirelength attains a minimum by gray coding;that was called the CT conjecture by Chavez and Trapp(Discrete...We study embeddings of the n-dimensional hypercube into the circuit with 2nvertices.We prove that the circular wirelength attains a minimum by gray coding;that was called the CT conjecture by Chavez and Trapp(Discrete Applied Mathematics,1998).This problem had claimed to be settled by Ching-Jung Guu in her doctoral dissertation“The circular wirelength problem for hypercubes”(University of California,Riverside,1997).Many argue there are gaps in her proof.We eliminate the gaps in her dissertation.展开更多
The exchanged hypercube EH(s, t) (where s ≥ 1 and t ≥ 1) is obtained by systematically reducing links from a regular hypercube Q,+t+l. One-step diagnosis of exchanged hypercubes which involves only one testi...The exchanged hypercube EH(s, t) (where s ≥ 1 and t ≥ 1) is obtained by systematically reducing links from a regular hypercube Q,+t+l. One-step diagnosis of exchanged hypercubes which involves only one testing phase during which processors test each other is discussed. The diagnosabilities of exchanged hypercubes are studied by using the pessimistic one-step diagno- sis strategy under two kinds of diagnosis models: the PMC model and the MM model. The main results presented here are the two proofs that the degree of diagnosability of the EH(s, t) under pessimistic one-step tl/tl fault diagnosis strategy is 2s where I ≤ s ≤ t (respectively, 2t, where 1 ≤ t ≤ s) based on the PMC model and that it is also 2s where 1 ≤ s ≤ t (respectively, 2t, where 1 ≤ t ≤ s) based on the MM* model.展开更多
Let Qn,k (n 〉 3, 1 〈 k ≤ n - 1) be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges, fv and fe be the numbers of faulty ve...Let Qn,k (n 〉 3, 1 〈 k ≤ n - 1) be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges, fv and fe be the numbers of faulty vertices and faulty edges, respectively. In this paper, we give three main results. First, a fault-free path P[u, v] of length at least 2n - 2fv - 1 (respectively, 2n - 2fv - 2) can be embedded on Qn,k with fv + f≤ n- 1 when dQn,k (u, v) is odd (respectively, dQ,~,k (u, v) is even). Secondly, an Q,,k is (n - 2) edgefault-free hyper Hamiltonianaceable when n ( 3) and k have the same parity. Lastly, a fault-free cycle of length at least 2n - 2fv can be embedded on Qn,k with f~ 〈 n - 1 and fv+f≤2n-4.展开更多
Compared with accurate diagnosis, the system’s selfdiagnosing capability can be greatly increased through the t/kdiagnosis strategy at most k vertexes to be mistakenly identified as faulty under the comparison model,...Compared with accurate diagnosis, the system’s selfdiagnosing capability can be greatly increased through the t/kdiagnosis 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/kdiagnosable. In this paper, based on the Maeng and Malek(MM)*model, a novel t/k-fault diagnosis(1≤k≤4) algorithm of ndimensional 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).展开更多
In this paper, we study the enhanced hypercube, an attractive variant of the hypercube and obtained by adding some complementary edges from a hypercube, and focus on cycles embedding on the enhanced hypercube with fau...In this paper, we study the enhanced hypercube, an attractive variant of the hypercube and obtained by adding some complementary edges from a hypercube, and focus on cycles embedding on the enhanced hypercube with faulty vertices. Let Fu be the set of faulty vertices in the n-dimensional enhanced hypercube Qn,k (n ≥ 3, 1 ≤ k 〈≤n - 1). When IFvl = 2, we showed that Qn,k - Fv contains a fault-free cycle of every even length from 4 to 2n - 4 where n (n ≥ 3) and k have the same parity; and contains a fault-free cycle of every even length from 4 to 2n - 4, simultaneously, contains a cycle of every odd length from n-k + 2 to 2^n-3 where n (≥ 3) and k have the different parity. Furthermore, when |Fv| = fv ≤ n - 2, we prove that there exists the longest fault-free cycle, which is of even length 2^n - 2fv whether n (n ≥ 3) and k have the same parity or not; and there exists the longest fault-free cycle, which is of odd length 2^n - 2fv + 1 in Qn,k - Fv where n (≥ 3) and k have the different parity.展开更多
The classical hypercube structure is a popular topological architecture in parallel computing environments and a large number of variations based on the hypercube were posed in the past three decades. Reliability eval...The classical hypercube structure is a popular topological architecture in parallel computing environments and a large number of variations based on the hypercube were posed in the past three decades. Reliability evaluation of systems is important to the design and maintenance of multiprocessor systems. The h-extra edge-connectivity of graph G(V, E) is a kind of measure for the reliability of interconnection systems, which is defined as the minimum cardinality of a subset of edge set, if any, whose deletion disconnects G and such that every re- maining component has at least h vertices. This paper shows that the h-extra edge-connectivity 2n-1 2n-1 of the hypercube Qn is a constant 2n-1 for 2n-1/3≤ h2n-1, and n ≥ 4, which extends the result of [Bounding the size of the subgraph induced by m vertices and extra edge-connectivity of hypercubes, Discrete Applied Mathematics, 2013, 161(16): 2753-2757].展开更多
In this paper we discuss a parallel sorting algorithm on a hypercube. Its time complexity is O(n logn/p) +O(n). Here, P is the number of processors available and n, the amount of items to be sorted. Take the problem o...In this paper we discuss a parallel sorting algorithm on a hypercube. Its time complexity is O(n logn/p) +O(n). Here, P is the number of processors available and n, the amount of items to be sorted. Take the problem of time-space optimization into consideration, when P≤ O(log n), this algorithm is both timespace optimal and cost optimization. But this means only speedup is O(P) and it is not linear speedup. Therefore, we further discuss relevant parallel efficiency problems.展开更多
Many routing protocols,such as distance vector and link-state protocols are used for nding the best paths in a network.To nd the path between the source and destination nodes where every node is visited once with no r...Many routing protocols,such as distance vector and link-state protocols are used for nding the best paths in a network.To nd the path between the source and destination nodes where every node is visited once with no repeats,Hamiltonian and Hypercube routing protocols are often used.Nonetheless,these algorithms are not designed to solve the problem of a node failure,where one or more nodes become faulty.This paper proposes an efcient modied Fault-free Hamiltonian Cycle based on the Hypercube Topology(FHCHT)to perform a connection between nodes when one or more nodes become faulty.FHCHT can be applied in a different environment to transmit data with a high-reliability connection by nding an alternative path between the source and destination nodes when some nodes fail.Moreover,a proposed Hamiltonian Near Cycle(HNC)scheme has been developed and implemented.HNC implementation results indicated that FHCHT produces alternative cycles relatively similar to a Hamiltonian Cycle for the Hypercube,complete,and random graphs.The implementation of the proposed algorithm in a Hypercube achieved a 31%and 76%reduction in cost compared to the complete and random graphs,respectively.展开更多
System-level fault identification is a key subject for maintaining the reliability of multiprocessor interconnected systems. This task requires fast and accurate inferences based on big volume of data, and the problem...System-level fault identification is a key subject for maintaining the reliability of multiprocessor interconnected systems. This task requires fast and accurate inferences based on big volume of data, and the problem of fault identification in an unstructured graph has been proved to be NP-hard (non-deterministic polynomial-time hard). In this paper, we adopt the PMC diagnostic model (first proposed by Preparata, Metze, and Chien) as the foundation of point-to-point probing technology, and a system contains only restricted-faults if every of its fault-free units has at least one fault-free neighbor. Under this condition we propose an efficient method of identifying restricted-faults in the folded hypercube, which is a promising alternative to the popular hypercube topology.展开更多
In this paper, we present an algorithm for embedding an m-sequential k-ary tree into its optimal hypercube with dilation at most 2 and prove its correctness.
Boolean homomorphisms of a hypercube, which correspond to the morphisms in the category of finite Boolean algebras, coincide with the linear isometries of the category of finite binary metric vector spaces.
Given a graph , a set is a resolving set if for each pair of distinct vertices there is a vertex such that . A resolving set containing a minimum number of vertices is called a minimum resolving set or a basis for . T...Given a graph , a set is a resolving set if for each pair of distinct vertices there is a vertex such that . A resolving set containing a minimum number of vertices is called a minimum resolving set or a basis for . The cardinality of a minimum resolving set is called the resolving number or dimension of and is denoted by . A resolving set is said to be a star resolving set if it induces a star, and a path resolving set if it induces a path. The minimum cardinality of these sets, denoted respectively by and are called the star resolving number and path resolving number. In this paper we investigate these re-solving parameters for the hypercube networks.展开更多
The diagnosability of a multiprocessor system or an interconnection network is an important research topic. The system and an interconnection network have an underlying topology, which is usually presented by a graph....The diagnosability of a multiprocessor system or an interconnection network is an important research topic. The system and an interconnection network have an underlying topology, which is usually presented by a graph. In this paper, we show proof for the g-good-neighbor diagnosability of the exchanged hypercube EH (s,t) under the PMC model and MM* model.展开更多
Abstract In this paper, the problem of fault tolerant routings in fault tolerant networks is considered. A routing in a network assigns to each ordered pair of nodes a fixed path. All communication among nodes must ...Abstract In this paper, the problem of fault tolerant routings in fault tolerant networks is considered. A routing in a network assigns to each ordered pair of nodes a fixed path. All communication among nodes must go on this routing. When either a node or a link in a fault tolerant network fails, the communication from one node to another using this faulty element must be sent via one or more intermediate nodes along a sequence of paths determined by this routing. An important and practical problem is how to choose a routing in the network such that intermediate nodes to ensure communication are small for any fault set. Let C d be a directed cycle of order d . In this paper. The author first discusses connectivity of Cartesian product digraphs, then proves that the Cartesian product digraph C d 1 ×C d 2 ×...×C d n (d i≥2,1≤i≤n) has a routing such that at most one intermediate node is needed to ensure transmission of messages among all non faulty nodes so long as the number of faults is less than n . This is a generalization of Dolev et al's result for the n dimensional cube.展开更多
Peer-to-peer (P2P) networking is a distributed architecture that partitions tasks or data between peer nodes. In this paper, an efficient Hypercube Sequential Matrix Partition (HS-MP) for efficient data sharing in P2P...Peer-to-peer (P2P) networking is a distributed architecture that partitions tasks or data between peer nodes. In this paper, an efficient Hypercube Sequential Matrix Partition (HS-MP) for efficient data sharing in P2P Networks using tokenizer method is proposed to resolve the problems of the larger P2P networks. The availability of data is first measured by the tokenizer using Dynamic Hypercube Organization. By applying Dynamic Hypercube Organization, that efficiently coordinates and assists the peers in P2P network ensuring data availability at many locations. Each data in peer is then assigned with valid ID by the tokenizer using Sequential Self-Organizing (SSO) ID generation model. This ensures data sharing with other nodes in large P2P network at minimum time interval which is obtained through proximity of data availability. To validate the framework HS-MP, the performance is evaluated using traffic traces collected from data sharing applications. Simulations conducting using Network simulator-2 show that the proposed framework outperforms the conventional streaming models. The performance of the proposed system is analyzed using energy consumption, average latency and average data availability rate with respect to the number of peer nodes, data size, amount of data shared and execution time. The proposed method reduces the energy consumption 43.35% to transpose traffic, 35.29% to bitrev traffic and 25% to bitcomp traffic patterns.展开更多
The design of new Satellite Launch Vehicle (SLV) is of interest, especially when a combination of Solid and Liquid Propulsion is included. Proposed is a conceptual design and optimization technique for multistage Lo...The design of new Satellite Launch Vehicle (SLV) is of interest, especially when a combination of Solid and Liquid Propulsion is included. Proposed is a conceptual design and optimization technique for multistage Low Earth Orbit (LEO) bound SLV comprising of solid and liquid stages with the use of Genetic Algorithm (GA) as global optimizer. Convergence of GA is improved by introducing initial population based on the Design of Experiments (DOE) Technique. Latin Hypercube Sampling (LHS)-DOE is used for its good space filling properties. LHS is a stratified random procedure that provides an efficient way of sampling variables from their multivariate distributions. In SLV design minimum Gross Lift offWeight (GLOW) concept is traditionally being sought. Since the development costs tend to vary as a function of GLOW, this minimum GLOW is considered as a minimum development cost concept. The design approach is meaningful to initial design sizing purpose for its computational efficiency gives a quick insight into the vehicle performance prior to detailed design.展开更多
Diagnosability of a multiprocessor system is an important measure of the reliability of interconnection networks.System-level diagnosis is a primary strategy to identify the faulty processors in a multiprocessor syste...Diagnosability of a multiprocessor system is an important measure of the reliability of interconnection networks.System-level diagnosis is a primary strategy to identify the faulty processors in a multiprocessor system.Based on a sound assumption proposed by Zhu et al.recently,we proposed a new diagnosability named non-inclusion diagnosability and showed that the non-inclusion diagnosability tN(Q_(n))of the hypercube under the PMC model is 2n-2.That is,assume that if two vertex sets Fi and F2 are both consistent with a syndrome and F_(1)C F_(2),then F2 is not the faulty set which we are looking for;the faulty set F is 1-step diagnosable if|F|≤2n-2 in Qn under the PMC model.展开更多
文摘We study embeddings of the n-dimensional hypercube into the circuit with 2nvertices.We prove that the circular wirelength attains a minimum by gray coding;that was called the CT conjecture by Chavez and Trapp(Discrete Applied Mathematics,1998).This problem had claimed to be settled by Ching-Jung Guu in her doctoral dissertation“The circular wirelength problem for hypercubes”(University of California,Riverside,1997).Many argue there are gaps in her proof.We eliminate the gaps in her dissertation.
基金Supported by the National Natural Science Foundation of China under Grant No.69933020 (国家自然科学基金) the Natural Science Foundation of Shandong Province of China under Grant No.Y2002G03 (山东省自然科学基金)
基金supported by the National Natural Science Fundation of China(61363002)
文摘The exchanged hypercube EH(s, t) (where s ≥ 1 and t ≥ 1) is obtained by systematically reducing links from a regular hypercube Q,+t+l. One-step diagnosis of exchanged hypercubes which involves only one testing phase during which processors test each other is discussed. The diagnosabilities of exchanged hypercubes are studied by using the pessimistic one-step diagno- sis strategy under two kinds of diagnosis models: the PMC model and the MM model. The main results presented here are the two proofs that the degree of diagnosability of the EH(s, t) under pessimistic one-step tl/tl fault diagnosis strategy is 2s where I ≤ s ≤ t (respectively, 2t, where 1 ≤ t ≤ s) based on the PMC model and that it is also 2s where 1 ≤ s ≤ t (respectively, 2t, where 1 ≤ t ≤ s) based on the MM* model.
基金supported by NSFC (11071096, 11171129)NSF of Hubei Province, China (T201103)
文摘Let Qn,k (n 〉 3, 1 〈 k ≤ n - 1) be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges, fv and fe be the numbers of faulty vertices and faulty edges, respectively. In this paper, we give three main results. First, a fault-free path P[u, v] of length at least 2n - 2fv - 1 (respectively, 2n - 2fv - 2) can be embedded on Qn,k with fv + f≤ n- 1 when dQn,k (u, v) is odd (respectively, dQ,~,k (u, v) is even). Secondly, an Q,,k is (n - 2) edgefault-free hyper Hamiltonianaceable when n ( 3) and k have the same parity. Lastly, a fault-free cycle of length at least 2n - 2fv can be embedded on Qn,k with f~ 〈 n - 1 and fv+f≤2n-4.
基金supported by the National Natural Science Foundation of China(61363002)
文摘Compared with accurate diagnosis, the system’s selfdiagnosing capability can be greatly increased through the t/kdiagnosis 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/kdiagnosable. In this paper, based on the Maeng and Malek(MM)*model, a novel t/k-fault diagnosis(1≤k≤4) algorithm of ndimensional 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).
基金supported by NSFC(11071096 and 11171129)Hubei Province,China(T201103)
文摘In this paper, we study the enhanced hypercube, an attractive variant of the hypercube and obtained by adding some complementary edges from a hypercube, and focus on cycles embedding on the enhanced hypercube with faulty vertices. Let Fu be the set of faulty vertices in the n-dimensional enhanced hypercube Qn,k (n ≥ 3, 1 ≤ k 〈≤n - 1). When IFvl = 2, we showed that Qn,k - Fv contains a fault-free cycle of every even length from 4 to 2n - 4 where n (n ≥ 3) and k have the same parity; and contains a fault-free cycle of every even length from 4 to 2n - 4, simultaneously, contains a cycle of every odd length from n-k + 2 to 2^n-3 where n (≥ 3) and k have the different parity. Furthermore, when |Fv| = fv ≤ n - 2, we prove that there exists the longest fault-free cycle, which is of even length 2^n - 2fv whether n (n ≥ 3) and k have the same parity or not; and there exists the longest fault-free cycle, which is of odd length 2^n - 2fv + 1 in Qn,k - Fv where n (≥ 3) and k have the different parity.
基金Supported by the National Natural Science Foundation of China(11171283,11471273,11461038,11301440)Natural Sciences Foundation of Shanxi Province(2014021010-2)
文摘The classical hypercube structure is a popular topological architecture in parallel computing environments and a large number of variations based on the hypercube were posed in the past three decades. Reliability evaluation of systems is important to the design and maintenance of multiprocessor systems. The h-extra edge-connectivity of graph G(V, E) is a kind of measure for the reliability of interconnection systems, which is defined as the minimum cardinality of a subset of edge set, if any, whose deletion disconnects G and such that every re- maining component has at least h vertices. This paper shows that the h-extra edge-connectivity 2n-1 2n-1 of the hypercube Qn is a constant 2n-1 for 2n-1/3≤ h2n-1, and n ≥ 4, which extends the result of [Bounding the size of the subgraph induced by m vertices and extra edge-connectivity of hypercubes, Discrete Applied Mathematics, 2013, 161(16): 2753-2757].
文摘In this paper we discuss a parallel sorting algorithm on a hypercube. Its time complexity is O(n logn/p) +O(n). Here, P is the number of processors available and n, the amount of items to be sorted. Take the problem of time-space optimization into consideration, when P≤ O(log n), this algorithm is both timespace optimal and cost optimization. But this means only speedup is O(P) and it is not linear speedup. Therefore, we further discuss relevant parallel efficiency problems.
文摘Many routing protocols,such as distance vector and link-state protocols are used for nding the best paths in a network.To nd the path between the source and destination nodes where every node is visited once with no repeats,Hamiltonian and Hypercube routing protocols are often used.Nonetheless,these algorithms are not designed to solve the problem of a node failure,where one or more nodes become faulty.This paper proposes an efcient modied Fault-free Hamiltonian Cycle based on the Hypercube Topology(FHCHT)to perform a connection between nodes when one or more nodes become faulty.FHCHT can be applied in a different environment to transmit data with a high-reliability connection by nding an alternative path between the source and destination nodes when some nodes fail.Moreover,a proposed Hamiltonian Near Cycle(HNC)scheme has been developed and implemented.HNC implementation results indicated that FHCHT produces alternative cycles relatively similar to a Hamiltonian Cycle for the Hypercube,complete,and random graphs.The implementation of the proposed algorithm in a Hypercube achieved a 31%and 76%reduction in cost compared to the complete and random graphs,respectively.
基金supported in part by the NSC under Grand No.NSC102-2221-E-468-018
文摘System-level fault identification is a key subject for maintaining the reliability of multiprocessor interconnected systems. This task requires fast and accurate inferences based on big volume of data, and the problem of fault identification in an unstructured graph has been proved to be NP-hard (non-deterministic polynomial-time hard). In this paper, we adopt the PMC diagnostic model (first proposed by Preparata, Metze, and Chien) as the foundation of point-to-point probing technology, and a system contains only restricted-faults if every of its fault-free units has at least one fault-free neighbor. Under this condition we propose an efficient method of identifying restricted-faults in the folded hypercube, which is a promising alternative to the popular hypercube topology.
基金Supported by the NNSF of Chitin(10301015)Supported by the Tianjia Planning Programs of Philosophy and Social Science of China(TJ05-TJ002)Supported by the Chitin Postdoctoral Science Foundayion(20060390169)
文摘In this paper, we present an algorithm for embedding an m-sequential k-ary tree into its optimal hypercube with dilation at most 2 and prove its correctness.
文摘Boolean homomorphisms of a hypercube, which correspond to the morphisms in the category of finite Boolean algebras, coincide with the linear isometries of the category of finite binary metric vector spaces.
文摘Given a graph , a set is a resolving set if for each pair of distinct vertices there is a vertex such that . A resolving set containing a minimum number of vertices is called a minimum resolving set or a basis for . The cardinality of a minimum resolving set is called the resolving number or dimension of and is denoted by . A resolving set is said to be a star resolving set if it induces a star, and a path resolving set if it induces a path. The minimum cardinality of these sets, denoted respectively by and are called the star resolving number and path resolving number. In this paper we investigate these re-solving parameters for the hypercube networks.
文摘The diagnosability of a multiprocessor system or an interconnection network is an important research topic. The system and an interconnection network have an underlying topology, which is usually presented by a graph. In this paper, we show proof for the g-good-neighbor diagnosability of the exchanged hypercube EH (s,t) under the PMC model and MM* model.
文摘Abstract In this paper, the problem of fault tolerant routings in fault tolerant networks is considered. A routing in a network assigns to each ordered pair of nodes a fixed path. All communication among nodes must go on this routing. When either a node or a link in a fault tolerant network fails, the communication from one node to another using this faulty element must be sent via one or more intermediate nodes along a sequence of paths determined by this routing. An important and practical problem is how to choose a routing in the network such that intermediate nodes to ensure communication are small for any fault set. Let C d be a directed cycle of order d . In this paper. The author first discusses connectivity of Cartesian product digraphs, then proves that the Cartesian product digraph C d 1 ×C d 2 ×...×C d n (d i≥2,1≤i≤n) has a routing such that at most one intermediate node is needed to ensure transmission of messages among all non faulty nodes so long as the number of faults is less than n . This is a generalization of Dolev et al's result for the n dimensional cube.
文摘Peer-to-peer (P2P) networking is a distributed architecture that partitions tasks or data between peer nodes. In this paper, an efficient Hypercube Sequential Matrix Partition (HS-MP) for efficient data sharing in P2P Networks using tokenizer method is proposed to resolve the problems of the larger P2P networks. The availability of data is first measured by the tokenizer using Dynamic Hypercube Organization. By applying Dynamic Hypercube Organization, that efficiently coordinates and assists the peers in P2P network ensuring data availability at many locations. Each data in peer is then assigned with valid ID by the tokenizer using Sequential Self-Organizing (SSO) ID generation model. This ensures data sharing with other nodes in large P2P network at minimum time interval which is obtained through proximity of data availability. To validate the framework HS-MP, the performance is evaluated using traffic traces collected from data sharing applications. Simulations conducting using Network simulator-2 show that the proposed framework outperforms the conventional streaming models. The performance of the proposed system is analyzed using energy consumption, average latency and average data availability rate with respect to the number of peer nodes, data size, amount of data shared and execution time. The proposed method reduces the energy consumption 43.35% to transpose traffic, 35.29% to bitrev traffic and 25% to bitcomp traffic patterns.
文摘The design of new Satellite Launch Vehicle (SLV) is of interest, especially when a combination of Solid and Liquid Propulsion is included. Proposed is a conceptual design and optimization technique for multistage Low Earth Orbit (LEO) bound SLV comprising of solid and liquid stages with the use of Genetic Algorithm (GA) as global optimizer. Convergence of GA is improved by introducing initial population based on the Design of Experiments (DOE) Technique. Latin Hypercube Sampling (LHS)-DOE is used for its good space filling properties. LHS is a stratified random procedure that provides an efficient way of sampling variables from their multivariate distributions. In SLV design minimum Gross Lift offWeight (GLOW) concept is traditionally being sought. Since the development costs tend to vary as a function of GLOW, this minimum GLOW is considered as a minimum development cost concept. The design approach is meaningful to initial design sizing purpose for its computational efficiency gives a quick insight into the vehicle performance prior to detailed design.
基金the National Natural Science Foundation of China(Nos.61672025,60974082,61179040 and 61075117)Shandong Provincial Natural Science Foundation(No.ZR2021MF012).
文摘Diagnosability of a multiprocessor system is an important measure of the reliability of interconnection networks.System-level diagnosis is a primary strategy to identify the faulty processors in a multiprocessor system.Based on a sound assumption proposed by Zhu et al.recently,we proposed a new diagnosability named non-inclusion diagnosability and showed that the non-inclusion diagnosability tN(Q_(n))of the hypercube under the PMC model is 2n-2.That is,assume that if two vertex sets Fi and F2 are both consistent with a syndrome and F_(1)C F_(2),then F2 is not the faulty set which we are looking for;the faulty set F is 1-step diagnosable if|F|≤2n-2 in Qn under the PMC model.