QoS路由中一种有效的多受限优化路径选择算法

1 引言目前,人们正期待着宽带集成服务网来支持各种各样的满足不同QoS要求的多媒体应用。在宽带体系结构的设计中的一个关键问题就是如何提供资源来满足每次连接的需求。毫无疑问,有效的QoS路由方案的建立是这种体系结构中的一个重要组成部分。的确,QoS路由已经成为许多研究的主题。人们已经认识到一个有效的QoS路由方案的建立给我们带来了许多挑战。在算法上,QoS路由带来的一个的挑战就是需要迅速地找到一条可行路径使它满足一组限制条件同时获得较高的网络资源利用率。一般而言,QoS路由是一个复杂的问题。首先,网络电话和分布式游戏等分布式应用在延迟、延迟抖动、丢失率和带宽等方面有许多不同的QoS限制。多个限制经常使得路由问题更加复杂。例如,寻找一条具有两个独立路径限制的可行路径是NP难的。其次,将来的集成服务网很可能既要传输QoS数据流又要传输尽力而为的数据,     

Precomputation for intra-domain QoS routing

Quality-of-service routing (QoSR), seeking to find a feasible path with multiple constraints, is an NP-complete problem. We propose a novel precomputation approach to multi-constrained intra-domain QoS routing (PMCP). It is assumed that a router maintains the link state information of the entire domain. PMCP cares each QoS weight to several degrees, and computes a number of QoS coefficients uniformly distributed in the multi-dimensional QoS metric space. Based on each coefficient, a linear QoS function is constructed to convert the multiple QoS metrics to a single QoS value. We then create a shortest path tree with respect to the QoS value by Dijkstra’s algorithm. Finally, according to the multiple coefficients, different shortest path trees are calculated to compose the QoS routing table. We analyze linear QoS functions in the QoS metric space, and give a mathematical model to determine the feasibility of a QoS request in the space. After PMCP is introduced, we analyze its computational complexity and present a method of QoS routing table lookup. Extensive simulations evaluate the performance of the proposed algorithm and present a comparative study.     

A survey on multi-constrained optimal path computation: Exact and approximate algorithms

The paper presents a survey on the techniques to solve the multi-constrained optimal path (MCOP) problem. Computing the MCOP is a task shared by many research areas, from transportation systems to telecommunication networks. In the latter, the MCOP is often related to the issue of Quality of Service (QoS) routing, which consists in finding a route between a couple of nodes that meets a series of QoS requirements such as bounded delay, packet loss, and other parameters. The MCOP problem has been faced by several authors and a plethora of solving methods is now available. In the present work, we draw the state of the art of exact and approximate MCOP computation algorithms, with particular attention to the networking area. We describe and analyse the most representative methods, and for each of them we derive the worst case computational complexity. In addition, we provide the reader with a uniform notation and with the detailed pseudo-code of various algorithms, so that the paper can indeed serve as a workable starting point for further studies on the MCOP problem.     

Shortest paths in euclidean graphs

We analyze a simple method for finding shortest paths inEuclidean graphs (where vertices are points in a Euclidean space and edge weights are Euclidean distances between points). For many graph models, the average running time of the algorithm to find the shortest path between a specified pair of vertices in a graph withV vertices andE edges is shown to beO(V) as compared withO(E +V logV) required by the classical algorithm due to Dijkstra.     

An efficient parallel strategy for the two-fixed-endpoint Hamiltonian path problem on distance-hereditary graphs

In this paper, we solve the two-fixed-endpoint Hamiltonian path problem on distance-hereditary graphs efficiently in parallel. Let T_d(|V|,|E|) and P_d(|V|,|E|) denote the parallel time and processor complexities, respectively, required to construct a decomposition tree of a distance-hereditary graph G=(V,E) on a PRAM model M_d. We show that this problem can be solved in O(T_d(|V|,|E|)+log|V|) time using O(P_d(|V|,|E|)+(|V|+|E|)/log|V|) processors on M_d. Moreover, if G is represented by its decomposition tree form, the problem can be solved optimally in O(log|V|) time using O((|V|+|E|)/log|V|) processors on an EREW PRAM. We also obtain a linear-time algorithm which is faster than the previous known O(|V|³) sequential algorithm.     

A Simpler and More Efficient Algorithm for the Next-to-Shortest Path Problem

Given an undirected graph G=(V,E) with positive edge lengths and two vertices s and t, the next-to-shortest path problem is to find an st-path which length is minimum amongst all st-paths strictly longer than the shortest path length. In this paper we show that the problem can be solved in linear time if the distances from s and t to all other vertices are given. Particularly our new algorithm runs in O(|V|log|V|+|E|) time for general graphs, which improves the previous result of O(|V|²) time and takes only linear time for unweighted graphs, planar graphs, and graphs with positive integer edge lengths.     

Computing Associative Functions Distributively in Spite of Link Failures

Repeated computation of associative functions is central to many asynchronous distributed algorithms reported in the literature. We present efficient distributed algorithms for computing associative functions in spite of undetectable link failures in non-partitioned distributed systems. Two distributed; algorithms are presented for function computation assuming that the distributed system is preprocessed by a one-time preprocessing step that uses O(|E| |V|) messages (where |E| and |V| are the number of links and the number of nodes of the system, respectively). The first algorithm tolerates single link failures using O(|V| log |V|) messages and the second algorithm, which is an extension of the first algorithm, copes with the simultaneous failure of k links using O(k|E| log |V|) messages. Efficient computation of associative functions in the presence of multiple link failures has been an open problem, and our work solves this open problem.     

Finding K shortest looping paths in a traffic-light network

In this paper we consider a traffic-light network where every node in the network is associated with the constraint consisting of a repeated sequence of time windows. The constraint aims to simulate the operations of traffic-light control in an intersection of roads. With this kind of constraints in place, directions of routes when passing through the intersections can be formally modeled. The objective of this paper is to find the first K shortest looping paths in the traffic-light network. An algorithm of time complexity of O(rK²|V₁|³) is developed, where r is the number of different windows of a node and |V₁| is the number of nodes in the original network.     

Efficient algorithms for regular expression constrained sequence alignment

Imposing constraints is an effective means to incorporate biological knowledge into alignment procedures. As in the PROSITE database, functional sites of proteins can be effectively described as regular expressions. In an alignment of protein sequences it is natural to expect that functional motifs should be aligned together. Due to this motivation, Arslan introduced the regular expression constrained sequence alignment problem and proposed an algorithm which, if implemented naïvely, can take time and space up to O(²|Σ|⁴|V|n²) and O(²|Σ|⁴|V|n), respectively, where Σ is the alphabet, n is the sequence length, and V is the set of states in an automaton equivalent to the input regular expression. In this paper we propose a more efficient algorithm solving this problem which takes O(³|V|n²) time and O(²|V|n) space in the worst case. If |V|=O(logn) we propose another algorithm with time complexity O(²|V|log|V|n²). The time complexity of our algorithms is independent of Σ, which is desirable in protein applications where the formulation of this problem originates; a factor of ²|Σ|=400 in the time complexity of the previously proposed algorithm would significantly affect the efficiency in practice.     

A factoring approach for the Steiner tree problem in undirected networks

In communication networks, many applications, such as video on demand and video conferencing, must establish a communications tree that spans a subset K in a vertex set. The source node can then send identical data to all nodes in set K along this tree. This kind of communication is known as multicast communication. A network optimization problem, called the Steiner tree problem (STP), is presented to find a least cost multicasting tree. In this paper, an O(|E|) algorithm is presented to find a minimum Steiner tree for series-parallel graphs where |E| is the number of edges. Based on this algorithm, we proposed an O(2^2c·|E|) algorithm to solve the Steiner tree problem for general graphs where c is the number of applied factoring procedures. The c value is strongly related to the topology of a given graph. This is quite different from other algorithms with exponential time complexities in |K|.     

The labeled perfect matching in bipartite graphs

In this paper, we deal with both the complexity and the approximability of the labeled perfect matching problem in bipartite graphs. Given a simple graph G=(V,E) with |V|=2n vertices such that E contains a perfect matching (of size n), together with a color (or label) function , the labeled perfect matching problem consists in finding a perfect matching on G that uses a minimum or a maximum number of colors.     

Mathematical models and routing algorithms for CAD technological preparation of cutting processes

Resource-conscious technologies for cutting sheet material include the ICP and ECP technologies that allow for aligning fragments of the contours of cutouts. In this work, we show the mathematical model for the problem of cutting out parts with these technologies and algorithms for finding cutting tool routes that satisfy technological constraints. We give a solution for the problem of representing a cutting plan as a plane graph G = (V,F,E), which is a homeomorphic image of the cutting plan. This has let us formalize technological constraints on the trajectory of cutting the parts according to the cutting plan and propose a series of algorithms for constructing a route in the graph G = (V,F,E), which is an image of an admissible trajectory. Using known coordinates of the preimages of vertices of graph G = (V,F,E) and the locations of fragments of the cutting plan that are preimages of edges of graph G = (V,F,E), the resulting route in the graph G = (V,E) can be interpreted as the cutting tool’s trajectory.The proposed algorithms for finding routes in a connected graph G have polynomial computational complexity. To find the optimal route in an unconnected graph G, we need to solve, for every dividing face f of graph G, a travelling salesman problem on the set of faces incident to f.     

Bipartite Matching in the Semi-streaming Model

We present the first deterministic 1+ε approximation algorithm for finding a large matching in a bipartite graph in the semi-streaming model which requires only O((1/ε)⁵) passes over the input stream. In this model, the input graph G=(V,E) is given as a stream of its edges in some arbitrary order, and storage of the algorithm is bounded by O(npolylog?n) bits, where $n = \lvert {V}\rvert $ . The only previously known arbitrarily good approximation for general graphs is achieved by the randomized algorithm of McGregor (Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and Randomization and Computation, Berkeley, CA, USA, pp. 170–181, 2005), which uses Ω((1/ε)^1/ε ) passes. We show that even for bipartite graphs, McGregor’s algorithm needs Ω(1/ε) ^Ω(1/ε) passes, thus it is necessarily exponential in the approximation parameter. The design as well as the analysis of our algorithm require the introduction of some new techniques. A novelty of our algorithm is a new deterministic assignment of matching edges to augmenting paths which is responsible for the complexity reduction, and gets rid of randomization. We repeatedly grow an initial matching using augmenting paths up to a length of 2k+1 for k=?2/ε?. We terminate when the number of augmenting paths found in one iteration falls below a certain threshold also depending on k, that guarantees a 1+ε approximation. The main challenge is to find those augmenting paths without requiring an excessive number of passes. In each iteration, using multiple passes, we grow a set of alternating paths in parallel, considering each edge as a possible extension as it comes along in the stream. Backtracking is used on paths that fail to grow any further. Crucial are the so-called position limits: when a matching edge is the ith matching edge in a path and it is then removed by backtracking, it will only be inserted into a path again at a position strictly lesser than i. This rule strikes a balance between terminating quickly on the one hand and giving the procedure enough freedom on the other hand.     

时延和时延差别受限的最大带宽多播路由分布式算法

本文采用反映网络实时特性的可用带宽代替代价作为第一度量，提出一种基于最大可用带宽路径且满足时延和时延差别约束的QoS实时多播路由分布式启发算法，该算法具有多项式复杂性，并通过分析得到每路径时延和二约束度量之间的关系，有效降低涉及时延和时延差别此类问题的复杂性。仿真实验证明，该算法具有较好的带宽性能。     

Complexity and design of QoS routing algorithms in wireless mesh networks

Quality of service (QoS) provisioning in wireless mesh networks (WMNs) is an open issue to support emerging multimedia services. In this paper, we study the problem of QoS provisioning in terms of end-to-end bandwidth allocation in WMNs. It is challenging due to interferences in the networks. We consider widely used interference models and show that except a few special cases, the problem of finding a feasible path is NP-complete under the models. We propose a k-shortest path based algorithmic framework to solve this problem. We also consider the problem of optimizing network performance by on-line dynamic routing, and adapt commonly used conventional QoS routing metrics to be used in WMNs. We find the optimal solutions for these problems through formulating them as optimization models. A model is developed to check the existence of a feasible path and another to find the optimal path for a demand; moreover, an on-line optimal QoS routing algorithm is developed. Comparing the algorithms implemented by the proposed framework with the optimization models shows that our solution can find existing feasible paths with high probability, efficiently optimizes path lengths, and has a comparable performance to the optimal QoS routing algorithm. Furthermore, our results show that contrary to wireline networks, minimizing resource consumption should be preferred over load distribution even in lightly loaded WMNs.     

A probabilistic algorithm for vertex connectivity of graphs

A probabilistic algorithm is presented which computes the vertex connectivity of an undirected graph G = (V,E) in expected time $\text{O((-log ε|V|}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{|E|)}$ with error probability at most e provided that |E|<frcase|1/2d|V|² for some universal constant d<1.     

Two flow network simplification algorithms

Flow network simplification can reduce the size of the flow network and hence the amount of computation performed by flow algorithms. We present the first linear time algorithm for the undirected network case. We also give an O(|E|∗(|V|+|E|)) time algorithm for the directed case, an improvement over the previous best O(|V|+²|E|log|V|) time solution. Both of our algorithms are quite simple.     

Stabilizing maximum matching in bipartite networks

A matching ${E_\mathcal{M}}$ of graph G =  (V, E) is a subset of the edges E, such that no vertex in V is incident to more than one edge in ${E_\mathcal{M}}$ . The matching ${E_\mathcal{M}}$ is maximum if there is no matching in G with size strictly larger than the size of ${E_\mathcal{M}}$ . In this paper, we present a distributed stabilizing algorithm for finding maximum matching in bipartite graphs based on the stabilizing PIF algorithm of Cournier et al. (Proceedings of 21st IEEE international conference on distributed computing systems, 91–98, 2001). Since our algorithm is stabilizing, it does not require initialization and withstands transient faults. The complexity of the proposed algorithm is O(d × n) rounds, where d is the diameter of the communication network and n is the number of nodes in the network. The space complexity is O(log Δ +  log d), where Δ is the largest degree of all the nodes in the communication network. In addition, an optimal version of the proposed algorithm finding maximum matching in linear time is also presented.     

基于蚂蚁算法的QoS分布式多播路由选择

采用启发式算法中蚂蚁算法解决包含带宽、时延和最小代价约束条件在内的分布式多播路由问题,基于蚂蚁具有找到蚁巢与食物之间的最短路径原理,并在分析QoS分布式多播路由的基础上,提出了一种基于蚁群算法的QoS分布式多播路由算法,仿真实验表明了该算法是合理的和有效的。