边故障[k]元[n]立方体的超级哈密顿交织性

[k]元[n]立方体（记为[Qkn]）是优于超立方体的可进行高效信息传输的互连网络之一。[Qkn]是一个二部图当且仅当[k]为偶数。令[G[V0,V1]]是一个二部图,若（1）任意一对分别在不同部的顶点之间存在一条哈密顿路,且（2）对于任意一点[v∈Vi],其中[i∈{0,1}],[V1-i]中任意一对顶点可以被[G[V0,V1]-v]中的一条哈密顿路相连,则图[G[V0,V1]]被称为是超级哈密顿交织的。因为网络中的元件发生故障是不可避免的,所以研究网络的容错性就尤为重要。针对含有边故障的[Qkn],其中[k4]是偶数且[n2],证明了当其故障边数至多为[2n-3]时,该故障[Qkn]是超级哈密顿交织图,且故障边数目的上界[2n-3]是最优的。     

Channel assignment with separation for interference avoidance in wireless networks

Given an integer /spl sigma/>1, a vector (/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/), of nonnegative integers, and an undirected graph G=(V, E), an L(/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/)-coloring of G is a function f from the vertex set V to a set of nonnegative integers, such that |f(u)-f(v)|/spl ges//spl delta//sub i/, if d(u,v)=i, for 1相似文献   

Conditional Edge-Fault Hamiltonicity of Matching Composition Networks

A graph G is called Hamiltonian if there is a Hamiltonian cycle in G. The conditional edge-fault Hamiltonicity of a Hamiltonian graph G is the largest k such that after removing k faulty edges from G, provided that each node is incident to at least two fault-free edges, the resulting graph contains a Hamiltonian cycle. In this paper, we sketch common properties of a class of networks, called matching composition networks (MCNs), such that the conditional edge-fault hamiltonicity of MCNs can be determined from the found properties. We then apply our technical theorems to determine conditional edge-fault hamiltonicities of several multiprocessor systems, including n-dimensional crossed cubes, n-dimensional twisted cubes, n-dimensional locally twisted cubes, n-dimensional generalized twisted cubes, and n-dimensional hyper Petersen networks. Moreover, we also demonstrate that our technical theorems can be applied to network construction.     

Fault-tolerant hamiltonian cycles and paths embedding into locally exchanged twisted cubes

The foundation of information society is computer interconnection network, and the key of information exchange is communication algorithm. Finding interconnection networks with simple routing algorithm and high fault-tolerant performance is the premise of realizing various communication algorithms and protocols. Nowadays, people can build complex interconnection networks by using very large scale integration (VLSI) technology. Locally exchanged twisted cubes, denoted by (s + t + 1)-dimensional LeTQ_s,t, which combines the merits of the exchanged hypercube and the locally twisted cube. It has been proved that the LeTQ_s,t has many excellent properties for interconnection networks, such as fewer edges, lower overhead and smaller diameter. Embeddability is an important indicator to measure the performance of interconnection networks. We mainly study the fault tolerant Hamiltonian properties of a faulty locally exchanged twisted cube, LeTQ_s,t − ( f_v + f_e), with faulty vertices f_v and faulty edges f_e. Firstly, we prove that an LeTQ_s,t can tolerate up to s−1 faulty vertices and edges when embedding a Hamiltonian cycle, for s≥2, t≥3, and s≤t. Furthermore, we also prove another result that there is a Hamiltonian path between any two distinct fault-free vertices in a faulty LeTQ_s,twith up to (s − 2) faulty vertices and edges. That is, we show that LeTQ_s,t is (s−1)-Hamiltonian and (s−2)- Hamiltonian-connected. The results are proved to be optimal in this paper with at most (s − 1)-fault-tolerant Hamiltonicity and (s − 2) fault-tolerant Hamiltonian connectivity of LeTQ_s,t.     

Routing algorithms on the bus-based hypercube network

In this paper, we study the properties of the bus-based hypercube, denoted as U(n,b), which is a kind of multiple-bus networks (MBN). U(n,b) consists of 2/sup n/ processors and 2/sup b/ buses, where 0 /spl les/ b /spl les/ n - 1, and each processor is connected to either /spl lceil/(b+2)/2/spl rceil/ or /spl lceil/(b+1)/2/spl rceil/ buses. We show that the diameter of U(n,b) is /spl lceil/(b-1)/2/spl rceil/ if b /spl ges/ 2. We also present an algorithm to select the best neighbor processor via which we can obtain one shortest routing path. In U(n,b), we show that if there exist some faults, the fault diameter DF(n,b,f) /spl les/ b+1, where f is the sum of bus faults and processor faults and 0 /spl les/ f /spl les/ /spl lceil/(b+3)/2/spl rceil/. Furthermore, we also show that the bus fault diameter DB(n,b,f) /spl les/ b/-2/spl rfloor/ - 3, where 0 /spl les/ f /spl les/ /spl lceil/(b-1)/2/spl rceil/ and f is the number of bus faults. These results improve significantly the previous result that DB(n,b,f) /spl les/ b - 2f + 1, where f is the number of bus faults.     

General-demand disjoint path covers in a graph with faulty elements

A k-disjoint path cover of a graph is a set of k internally vertex-disjoint paths which cover the vertex set with k paths and each of which runs between a source and a sink. Given that each source and sink v is associated with an integer-valued demand d(v)≥1, we are concerned with general-demand k-disjoint path cover in which every source and sink v is contained in the d(v) paths. In this paper, we present a reduction of a general-demand disjoint path cover problem to an unpaired many-to-many disjoint path cover problem, and obtain some results on disjoint path covers of restricted HL-graphs and proper interval graphs with faulty vertices and/or edges.     

Constructing edge-disjoint spanning trees in product networks

A Cartesian product network is obtained by applying the cross operation on two graphs. We study the problem of constructing the maximum number of edge-disjoint spanning trees (abbreviated to EDSTs) in Cartesian product networks. Let G=(V/sub G/, E/sub G/) be a graph having n/sub 1/ EDSTs and F=(V/sub F/, E/sub F/) be a graph having n/sub 2/ EDSTs. Two methods are proposed for constructing EDSTs in the Cartesian product of G and F, denoted by G/spl times/F. The graph G has t/sub 1/=|E/sub G/|/spl middot/n/sub 1/(|V/sub G/|-1) more edges than that are necessary for constructing n/sub 1/ EDSTs in it, and the graph F has t2=|E/sub F/'-n/sub 2/(|V/sub F/|-1) more edges than that are necessary for constructing n/sub 2/ EDSTs in it. By assuming that t/sub 1//spl ges/n/sub 1/ and t/sub 2//spl ges/n/sub 2/, our first construction shows that n/sub 1/+n/sub 2/ EDSTS can be constructed in G/spl times/F. Our second construction does not need any assumption and it constructs n/sub 1/+n/sub 2/-1 EDSTs in G/spl times/F. By applying the proposed methods, it is easy to construct the maximum numbers of EDSTs in many important Cartesian product networks, such as hypercubes, tori, generalized hypercubes, mesh connected trees, and hyper Petersen networks.     

L/sup p/ approximation of Sigma-Pi neural networks

A feedforward Sigma-Pi neural network with a single hidden layer of m neurons is given by /sup m//spl Sigma//sub j=1/c/sub j/g(n/spl Pi//sub k=1/x/sub k/-/spl theta//sub k//sup j///spl lambda//sub k//sup j/) where c/sub j/, /spl theta//sub k//sup j/, /spl lambda//sub k//spl isin/R. We investigate the approximation of arbitrary functions f: R/sup n//spl rarr/R by a Sigma-Pi neural network in the L/sup p/ norm. An L/sup p/ locally integrable function g(t) can approximate any given function, if and only if g(t) can not be written in the form /spl Sigma//sub j=1//sup n//spl Sigma//sub k=0//sup m//spl alpha//sub jk/(ln|t|)/sup j-1/t/sub k/.     

A fast fault-identification algorithm for bijective connection graphs using the PMC model

Diagnosis of reliability is an important topic for interconnection networks. Under the classical PMC model, Dahura and Masson [5] proposed a polynomial time algorithm with time complexity O(N^2.5) to identify all faulty nodes in an N-node network. This paper addresses the fault diagnosis of so called bijective connection (BC) graphs including hypercubes, twisted cubes, locally twisted cubes, crossed cubes, and Möbius cubes. Utilizing a helpful structure proposed by Hsu and Tan [20] that was called the extending star by Lin et al. [24], and noting the existence of a structured Hamiltonian path within any BC graph, we present a fast diagnostic algorithm to identify all faulty nodes in O(N) time, where N = 2ⁿ, n ? 4, stands for the total number of nodes in the n-dimensional BC graph. As a result, this algorithm is significantly superior to Dahura–Masson’s algorithm when applied to BC graphs.     

Remarks on the L/sup p/-input converging-state property

Let X /spl sub/ /spl Ropf//sup N/ and consider a system x/spl dot/ = f(x,u), f : X /spl times/ /spl Ropf//sup M/ /spl rarr/ /spl Ropf//sup N/, with the property that the associated autonomous system x/spl dot/ = f (x,0) has an asymptotically stable compactum C with region of attraction A. Assume that x is a solution of the former, defined on [0,/spl infin/), corresponding to an input function u. Assume further that, for each compact K /spl sub/ X, there exists k > 0 such that |f(z,v) - f(z,0)| /spl les/ k|v| for all (z,v) /spl isin/ /spl times/ /spl Ropf//sup M/. A simple proof is given of the following L/sup p/-input converging-state property: if u /spl isin/ L/sup p/ for some p /spl isin/ [1,/spl infin/) and x has an /spl omega/-limit point in A, then x approaches C.     

Fault-tolerant analysis of a class of networks

In this paper, we explore the 2-extraconnectivity of a special class of graphs G(G₀,G₁;M) proposed by Chen et al. [Y.-C. Chen, J.J.M. Tan, L.-H. Hsu, S.-S. Kao, Super-connectivity and super edge-connectivity for some interconnection networks, Applied Mathematics and Computation 140 (2003) 245-254]. As applications of the results, we obtain that the 2-extraconnectivities of several well-known interconnection networks, such as hypercubes, twisted cubes, crossed cubes, Möbius cubes and locally twisted cubes, are all equal to 3n−5 when their dimension n is not less than 8. That is, when n?8, at least 3n−5 vertices must be removed to disconnect any one of these n-dimensional networks provided that the removal of these vertices does not isolate a vertex or an edge.     

Optimal Embeddings of Paths with Various Lengths in Twisted Cubes

Twisted cubes are variants of hypercubes. In this paper, we study the optimal embeddings of paths of all possible lengths between two arbitrary distinct nodes in twisted cubes. We use TQ_n to denote the n-dimensional twisted cube and use dist(TQ_n, u, v) to denote the distance between two nodes u and v in TQ_n, where n ges l is an odd integer. The original contributions of this paper are as follows: 1) We prove that a path of length l can be embedded between u and v with dilation 1 for any two distinct nodes u and v and any integer l with dist(TQ_n, u, v) + 2 les l les 2ⁿ - 1 (n ges 3) and 2) we find that there exist two nodes u and v such that no path of length dist(TQ_n, u, v) + l can be embedded between u and v with dilation 1 (n ges 3). The special cases for the nonexistence and existence of embeddings of paths between nodes u and v and with length dist(TQ_n, u, v) + 1 are also discussed. The embeddings discussed in this paper are optimal in the sense that they have dilation 1     

Hamiltonicity of the WK-recursive network with and without faulty nodes

Recently, the WK-recursive network has received much attention due to its many favorable properties such as a high degree of scalability. By K(d,t), we denote the WK-recursive network of level t, each of whose basic modules is a d-node complete graph, where d>1 and t/spl ges/1. In this paper, we first show that K(d,t) is Hamiltonian-connected, where d/spl ges/4. A network is Hamiltonian-connected if it contains a Hamiltonian path between every two distinct nodes. In other words, a Hamiltonian-connected network can embed the longest linear array between any two distinct nodes with dilation, congestion, load, and expansion all equal to one. Then, we construct fault-free Hamiltonian cycles in K(d,t) with at most d-3 faulty nodes, where d/spl ges/4. Since the connectivity of K(d,t) is d-1, the result is optimal.     

Longest fault-free paths in hypercubes with vertex faults

The hypercube is one of the most versatile and efficient interconnection networks (networks for short) so far discovered for parallel computation. Let f denote the number of faulty vertices in an n-cube. This study demonstrates that when f ? n − 2, the n-cube contains a fault-free path with length at least 2ⁿ − 2f − 1 (or 2ⁿ − 2f − 2) between two arbitrary vertices of odd (or even) distance. Since an n-cube is a bipartite graph with two partite sets of equal size, the path is longest in the worst-case. Furthermore, since the connectivity of an n-cube is n, the n-cube cannot tolerate n − 1 faulty vertices. Hence, our result is optimal.     

Strongly Hamiltonian laceability of the even k-ary n-cube

The interconnection network considered in this paper is the k-ary n-cube that is an attractive variance of the well-known hypercube. Many interconnection networks can be viewed as the subclasses of the k-ary n-cubes include the cycle, the torus and the hypercube. A bipartite graph is Hamiltonian laceable if there exists a Hamiltonian path joining every two vertices which are in distinct partite sets. A bipartite graph G is strongly Hamiltonian laceable if it is Hamiltonian laceable and there exists a path of length N − 2 joining each pair of vertices in the same partite set, where N = |V(G)|. We prove that the k-ary n-cube is strongly Hamiltonian laceable for k is even and n  2.     

Edge congestion and topological properties of crossed cubes

An n-dimensional crossed cube, CQ_n, is a variation of hypercubes. In this paper, we give a new shortest path routing algorithm based on a new distance measure defined herein. In comparison with Efe's algorithm, which generates one shortest path in O(n²) time, our algorithm can generate more shortest paths in O(n) time. Based on a given shortest path routing algorithm, we consider a new performance measure of interconnection networks called edge congestion. Using our shortest path routing algorithm and assuming that message exchange between all pairs of vertices is equally probable, we show that the edge congestion of crossed cubes is the same as that of hypercubes. Using the result of edge congestion, we can show that the bisection width of crossed cubes is 2^n-1. We also prove that wide diameter and fault diameter are [n/2]+2. Furthermore, we study embedding of cycles in cross cubes and construct more types than previous work of cycles of length at least four     

Should model-based inverse inputs be used as feedforward under plant uncertainty?

Bounds on the size of the plant uncertainties are found such that the use of the inversion-based feedforward input improves the output-tracking performance when compared to the use of feedback alone. The output-tracking error is normalized by the size of the desired output and used as a measure of the output tracking performance. The worst-case performance is compared for two cases: (1) with the use of feedback alone and (2) with the addition of the feedforward input. It is shown that inversion-based feedforward controllers can lead to performance improvements at frequencies w where the uncertainty /spl Delta/ (jw) in the nominal plant is smaller than the size of the nominal plant G/sub 0/(jw) divided by its condition number K/sub G0/ (jw), i.e., /spl par//spl Delta/(jw)/spl par//sub 2/ < /spl par/G/sub 0/(jw) /spl par//sub 2//k/sub G0/ (jw). A modified feedforward input is proposed that only uses the model information in frequency regions where plant uncertainty is sufficiently small. The use of this modified inverse with (any) feedback results in improvement of the output tracking performance, when compared to the use of the feedback alone.     

泡形互连网络的条件连通性度量

n维泡形网络是设计大规模多处理机系统时最常用的互连网络拓扑结构之一,它以n维泡形图Bn为数学模型。F是连通图G的顶点子集,使得G-F不再连通且G-F的每个连通分支都有至少有n个顶点的F的势叫做G的Rk连通度。Rk连通度是衡量网络可靠性的一个重要参数。一般来说,网络的Rk连通度越大,其可靠性越高。研究了n维泡形网络的 k连通性;证明了在n维泡形网络中,当n≥3时,其R1连通度为2n-4;当n≥4 时,其R2连通度为4n-12。     

Optimal algorithms for the channel-assignment problem on a reconfigurable array of processors with wider bus networks

The computation model on which the algorithms are developed is the reconfigurable array of processors with wider bus networks (abbreviated to RAPWBN). The main difference between the RAPWBN model and other existing reconfigurable parallel processing systems is that the bus width of each network is bounded within the range [2,[/spl radic/(N)]]. Such a strategy not only saves the silicon area of the chip as well as increases the computational power enormously, but the strategy also allows the execution speed of the proposed algorithms to be tuned by the bus bandwidth. To demonstrate the computational power of the RAPWBN, the channel-assignment problem is derived in this paper. For the channel-assignment problem with N pairs of components, we first design an O(T + [N//spl omega/]) time parallel algorithm using 2N processors with a 2N-row by 2N-column bus network, where the bus width of each bus network is /spl omega/-bit for 2 /spl les/ /spl omega/ /spl les/ [/spl radic/N] and T = [log/sub /spl omega//N] + 1. By tuning the bus bandwidth to the natural log N-bit and the extended N/sup 1/c/-bit (N/sup 1/c/ > log N) for any constant c and c /spl ges/ 1, two more results which run in O(log N/log log N) and O(1) time, respectively, are also derived. When compared to the algorithms proposed by Olariu et al. [17] and Lin [14], it is shown that our algorithm runs in the equivalent time complexity while significantly reducing the number of processors to O(N).     

Minimum neighborhood in a generalized cube

Generalized cubes are a subclass of hypercube-like networks, which include some hypercube variants as special cases. Let θG(k) denote the minimum number of nodes adjacent to a set of k vertices of a graph G. In this paper, we prove for each n-dimensional generalized cube and each integer k satisfying n+2?k?2n. Our result is an extension of a result presented by Fan and Lin [J. Fan, X. Lin, The t/k-diagnosability of the BC graphs, IEEE Trans. Comput. 54 (2) (2005) 176-184].