一种计算Ad hoc网络K-终端可靠性的线性时间算法

研究计算Ad hoe网络K-终端可靠性的线性时间算法,可以快速计算Ad hoe网络K-终端可靠性。为了计算Ad hoe网络分级结构尽终端可靠性,可以采用无向概率图表示Ad hoe网络的分级结构。每个簇头由已知失效率的结点表示,并且当且仅当两个簇相邻时,两个结点间的互连由边表示。这个概率图的链路完全可靠,并且已知结点的失效率。此图的K-终端可靠性为给定K-结点集是互连的概率。文中提出了基于合适区间图计算尽终端可靠性的一种线性时间算法。本算法可用来计算Ad hoe网络的K-终端可靠性。其时间复杂度为O（｜V｜＋｜E｜）。     

A Cutset Approach to Reliability Evaluation in Communication Networks

A global reliability measure called 'network reliability' (NR) is the probability that a call entering a probabilistic network at any originating node can reach every other node. This concept is quite useful in multiterminal networks such as computer networks and parallel processors, etc. A simple technique is presented for evaluating NR in symbolic form. The method is based on cutsets and is computationally advantageous with respect to the spanning tree approach. It requires fewer cutsets to be manipulated in the process of determining the NR expression. The number of cutsets is approximately half that of spanning trees even for a small sized computer communication network and there is a further improvement in the situation for larger networks.     

Polygon-to-chain reductions work for networks with imperfect vertices

One of the techniques known as the Polygon-to-Chain reductions for computing the terminal reliabilities of networks with perfect vertices is generalised for computing the terminal reliabilities of networks with imperfect vertices. The necessary reduction formulas and new vertex/edge reliabilities are established. Consequently, the terminal reliabilities of any series-parallel network with imperfect vertices can also be computed in linear time. This extends a result of Satyanarayana and Wood on the case where all vertices are perfect.     

Computing 2-terminal reliability for radio-broadcast networks

The authors present a probabilistic graph model for radio broadcast networks where nodes fail randomly and the edges are perfectly reliable. This model can represent the general case where both the nodes and edges can fail. Using this model, it is shown that the two-terminal reliability problem for radio broadcast networks is computationally difficult, in particular #P-complete, even in two important restricted cases. Efficient bounding techniques based on subgraph counts and vertex-packing methods are presented. The subgraph counting and vertex-packing bounds are the counterparts of the subgraph counting and edge-packing bounds for wired point-to-point networks with reliable nodes and unreliable links. The authors define series and parallel node reductions for arbitrary networks with unreliable nodes and reliable edges, and they incorporate these reductions into a new polynomial-time algorithm to improve the vertex-packing bounds via approximation by series-parallel reducible graphs     

边失效概率不同情况下网络全终端可靠度的近似计算

用可靠性多项式计算网络全终端可靠度是评估网络拓扑结构德定程度的重要依据,精确计算可靠性多项式是一个NP-hard问题.本文通过对基于产生孤立点的概率随机事件的定义,运用概率不等式变换,给出了点可靠、边以不同的概率相互独立失效时,网络全终端可靠度的上界表达式,在可靠度近似计算过程中避免了对网络边割集和路集的搜索.最后,在...     

End-to-end data paths: quickest or most reliable?

Let N=(V,E,c,l,p) be a network where V is the set of n vertices, E is the set of m edges, c(u,v)⩾0 is the capacity of edge {u,v}, l(u,v)⩾0 is the delay of edge {u,v}, p(u,v)∈[0,1] is the operational probability of edge {u,v}. In this letter, we present O(rm+rnlog n) time algorithms for the most reliable quickest path problem and the quickest most reliable path problem, where r is the number of different capacity values in the network     

Factoring and reductions for networks with imperfect vertices

Factoring and reductions are effective methods for computing the K-terminal reliability of undirected networks, but they have been applied mostly to networks with perfect vertices. However, in real problems, vertices may fail as well as edges. Imperfect vertices can be factored like edges, but the complexity then increases exponentially with their number. A technique has been developed to account for the failure of vertices with small additional cost, using a modified method of factoring and reductions. This technique is very easy to integrate into a factoring algorithm. It consists of factoring not on a single element (e.g., a single edge) but on a set of elements (e.g., an edge and its endpoints). The problem is that random variables associated with the elements of the network are no longer independent. This can be handled by choosing factoring edges that have at least one perfect endpoint. This technique leaves the factoring algorithm practically unchanged. The only difference is that some supplementary probability values are kept for the imperfect vertices of the original and the induced graphs. For algorithms using simple reductions, it has negligible computational cost     

A New Algorithm for the Reliability Analysis of Multi-Terminal Networks

In a probabilistic network, source-to-multiple-terminal reliability (SMT reliability) is the probability that a specified vertex can reach every other vertex. This paper derives a new topological formula for the SMT reliability of probabilistic networks. The formula generates only non-cancelling terms. The non-cancelling terms in the reliability expression correspond one-to-one with the acyclic t-subgraphs of the network. An acyclic t-subgraph is an acyclic graph in which every link is in at least one spanning rooted tree of the graph. The sign to be associated with each term is easily computed by counting the vertices and links in the corresponding subgraph. Overall reliability is the probability that every vertex can reach every other vertex in the network. For an undirected network, it is shown the SMT reliability is equal to the overall reliability. The formula is general and applies to networks containing directed or undirected links. Furthermore link failures in the network can be s-dependent. An algorithm is presented for generating all acyclic t-subgraphs and computing the reliability of the network. The reliability expression is obtained in symbolic factored form.     

通信网中链路重要性的评价方法

本文提出了一种通信网链路重要性的评价方法,该方法可以评价全网范围内的链路重要性.最重要的链路是将其进行边收缩操作后,得到的图的生成树数目最多.通过比较生成树的数目,我们可以判断通信网中任意两条链路的相对重要性.基于生成树数目的边收缩方法反映了某条链路处于正常工作时,对整个通信网的贡献大小.实验结果和理论分析均证明了该方法的有效性和可行性.     

Reliability polynomials and link importance in networks

The reliability polynomial is a graph invariant which is of interest where graphs are used as models of systems such as communication networks, computer networks, and transportation networks. This paper examines the use of reliability polynomials to rank the edges in a graph in terms of overall importance to graph reliability. For a given edge e in the graph G, G-e and G*e denote the graph with the link deleted and contracted (respectively); p (0相似文献   

Efficient and Exact Reliability Evaluation for Networks With Imperfect Vertices

The factoring theorem, and BDD-based algorithms have been shown to be efficient reliability evaluation methods for networks with perfectly reliable vertices. However, the vertices, and the links of a network may fail in the real world. Imperfect vertices can be factored like links, but the complexity increases exponentially with their number. Exact algorithms based on the factoring theorem can therefore induce great overhead if vertex failures are taken into account. To solve the problem, a set of exact algorithms is presented to deal with vertex failures with little additional overhead. The algorithms can be used to solve terminal-pair, k-terminal, and all-terminal reliability problems in directed, and undirected networks. The essential variable is defined to be a vertex or a link of a network whose failure has the dominating effect on network reliability. The algorithms are so efficient that it takes less than 1.2 seconds on a 1.67 GHz personal computer to identify the essential variable of a network having 2⁹⁹ paths. When vertex failures in a 3 times 10 mesh network are taken into account, the proposed algorithms can induce as little as about 0.3% of runtime overhead, while the best result from factoring algorithms incurs about 300% overhead     

A linear-time algorithm for computing K-terminal reliability onproper interval graphs

Consider a probabilistic graph in which the edges are perfectly reliable, but vertices can fail with some known probabilities. The K-terminal reliability of this graph is the probability that a given set of vertices K is connected. This reliability problem is #P-complete for general graphs, and remains #P-complete for chordal graphs and comparability graphs. This paper presents a linear-time algorithm for computing K-terminal reliability on proper interval graphs. A graph G = (V, E) is a proper interval graph if there exists a mapping from V to a class of intervals I of the real line with the properties that two vertices in G are adjacent if their corresponding intervals overlap and no interval in I properly contains another. This algorithm can be implemented in O(|V| + |E|) time     

Bounding network-reliability using consecutive minimal cutsets

A subset of consecutive minimal cutsets of the set of cutsets is used to develop an efficient algorithm to compute an upper bound for the reliability of a network. The reliability is the probability that a path consisting only of functioning arcs exists between the source and the sink of the network. The nodes of this network are perfect, but the arcs are independent and either function or fail with known probabilities. For the case of source-to-sink planar networks, an approach to obtain a lower bound for the reliability of the network is also presented. Examples illustrate the use of the algorithm and show that the upper bound is, is many cases, better than that obtained by A.W. Shogan (1976)     

Steiner trees in probabilistic networks

Various network reliability problems are #P-complete, however, certain classes of networks such as series-parallel networks, admit polynomial time algorithms. We extend these efficient methods to a superclass of series-parallel networks, the partial 2-trees. In fact, we solve a more general problem: given a probabilistic partial 2-tree and a set T of target nodes, we compute in linear time the probability of obtaining a subgraph connecting all of the target nodes. Equivalently, this is the probability of obtaining a Steiner tree for T. The algorithm exploits a characterization of partial 2-trees as graphs with no subgraph homeomorphic to K₄.     

Factoring Algorithms for Computing K-Terminal Network Reliability

Let GK denote a graph G whose edges can fail and with a set K ? V specified. Edge failures are independent and have known probabilities. The K-terminal reliability of GK, R(GK), is the probability that all vertices in K are connected by working edges. A factoring algorithm for computing network reliability recursively applies the formula R(GK) = piR(GK * ei) + qiR(GK - ei) where GK * ei is GK, with edge ei contracted, GK - ei is GK with ei deleted and pi ? 1 - qi is the reliability of edge ei. Various reliability-preserving reductions can be performed after each factoring operation in order to reduce computation. A unified framework is provided for complexity analysis and for determining optimal factoring strategies. Recent results are reviewed and extended within this framework.     

A practical implementation of the factoring theorem for networkreliability

The factoring theorem is a simple tool for determining the K -terminal reliability of a network, i.e. the probability that a given set K of terminals in the network are connected to each other by a path of working edges. An implementation of an algorithm which uses the factoring theorem, in conjunction with degree-1 and degree-2 vertex reductions, to determine the reliability of a network is presented. Networks treated have completely reliable nodes and have edges which fail statistically and independently with known probabilities. The reliability problem is to determine the probability that all nodes in a designated set of nodes can communicate with each other. Such an implementation of the factoring theorem can be incorporated in a small, stand-alone program of about 500 lines of code. A program of this type requires little computer memory and is ideally suited for microcomputer use     

K-terminal reliability in ring networks

The authors present a new formula for computing K-terminal reliability in a communication network whose stations and links (vertices and edges) form a network graph G having a ring topology, where K-terminal reliability is the probability R_K(G) that a subset of R specific terminal stations in G can communicate. This new formula is applied to three Fiber Distributed Data Interface (FDDI) ring-network topologies, and for each topology the authors derive closed-form polynomial expressions of R_K(G) in terms of the failure probabilities of links, network ports, and station common units. The authors define the concept of the K-minimal Eulerian circuit and use combinations of these circuits to obtain K-graphs and their resulting dominations, thus extending the use of K-graphs to ring networks in which data messages, tokens, or other control frames traverse operative network links with an Eulerian tour. Distinct K-graphs having a nonzero sum of dominations are called noncanceled K-graphs and correspond exactly to terms in closed-form polynomial expressions of R_K(G). The authors show that trees have only one K-graph and that counter-rotating dual rings and rings of trees have at most 2K+1 noncanceled R-graphs. These results contribute the first closed-form polynomial R-terminal reliability expressions for the ring-of-trees topology. The results are useful in evaluating dependability, reliability, availability, or survivability of token rings and similar networks     

On the reliability of a number of s-p reducible graphs

Let G=(V,E) be a graph whose edges may fail with known probabilities and let K a subset of V be specified. The overall reliability of G, denoted by R(G), is the probability that all vertices in K=V communicate with each other. We have two types of graphs, s-p reducible and s-p complex, depending on whether after series-arallel reductions the result is a single edge or not. A number of s-p reducible graphs are presented and expressions that evaluate their overall reliability are introduced.     

On Crossbar Switching Networks

For networks that exhibit neither concentration nor expansion, the well-known probabilistic model of C. Y. Lee is refined so as to take account of the dependence of events in different stages. For series-parallel networks, the refined model yields exact expressions for the point-to-point blocking probability. These expressions bear the same relationship to the refined model as the KittredgeMolina expressions do to Lee's model. Comparison between the two sets of expressions shows that Lee's model tends to overestimate the blocking probability. Asymptotic analysis of the new expressions leads to improved upper bounds on the cost: it is shown that a network that carriesNerlangs with a blocking probability at mostepsilon > 0can be built with6N log_{2} N + O(N log log 1/epsilon)contacts.