覆盖组播的最小覆盖代价路由算法

与IP组播相比,覆盖组播通常会消耗更多的底层网络资源。因此,在覆盖网中构造组播转发树时,考虑合理地利用底层网络资源具有一定的实际意义。给出覆盖代价的概念,把覆盖组播路由问题归结为求无向完全图的度和延迟受限、具有最小覆盖代价的生成树问题,求解的目标是在满足应用需求和端用户主机性能要求的同时使所消耗的底层网络资源最少。给出了求解该问题的启发式遗传算法,通过仿真实验验证了该算法的有效性。     

A note on distributed multicast routing in point-to-point networks

The distributed algorithm for a multicast connection set-up, based on the ‘cheapest insertion’ heuristic, is reviewed. The multicast routing problem is translated into a Steiner tree problem in point-to-point networks where nodes have only a limited knowledge about the network. A solution is proposed in which the time complexity and the amount of information exchanged between network nodes are proportional to the number of members of the multicast group. The Steiner tree is constructed by means of a distributed table-passing algorithm. The analysis of the algorithm presented, backed up by simulation results, confirms its superiority over the algorithm based on ‘waving technique’.Scope and purposeMulticasting is a mechanism used in communication networks that allows distribution of information from a single source to multiple destinations. The problem of finding a multicast connection for a static group of communicating entities in connection-oriented point-to-point network can be formulated in graph theory as a minimum Steiner tree problem. Due to NP-completeness of the Steiner tree problem multicast, routing algorithms are based on heuristics. The diversity of network environments and the lack of centralised information about network topology require an effective distribution of the multicast routing algorithms among the network nodes. This article presents an alternative to the distributed algorithm proposed by Rugelj and Klavzar that implements the same heuristics for the construction of a minimum cost multicast connection in point-to-point networks. The present algorithm constitutes a substantial improvement over that previously proposed with regard to running time and the amount of the information exchanged between network nodes.     

A Polynomial Time Approximation Scheme for Minimum Cost Delay-Constrained Multicast Tree under a Steiner Topology

This paper is concerned with a restricted version of minimum cost delay-constrained multicast in a network where each link has a delay and a cost. Given a source vertex $s$ and $p$ destination vertices $t_1, t_2, \ldots, t_p$ together with $p$ corresponding nonnegative delay constraints $d_1, d_2, \ldots, d_p$, many QoS multicast problems seek a minimum cost multicast tree in which the delay along the unique $s$--$t_i$ path is no more than $d_i$ for $1 \le i \le p$. This problem is NP-hard even when the topology of the multicast tree is fixed. In this paper we show that every multicast tree has an underlying Steiner topology and that every minimum cost delay-constrained multicast tree corresponds to a minimum cost delay-constrained realization of a corresponding Steiner topology. We present a fully polynomial time approximation scheme for computing a minimum cost delay-constrained multicast tree under a Steiner topology. We also present computational results of a preliminary implementation to illustrate the effectiveness of our algorithm and discuss its applications.     

A Polynomial Time Approximation Scheme for Minimum Cost Delay-Constrained Multicast Tree under a Steiner Topology

This paper is concerned with a restricted version of minimum cost delay-constrained multicast in a network where each link has a delay and a cost. Given a source vertex $s$ and $p$ destination vertices $t_1, t_2, \ldots, t_p$ together with $p$ corresponding nonnegative delay constraints $d_1, d_2, \ldots, d_p$, many QoS multicast problems seek a minimum cost multicast tree in which the delay along the unique $s$--$t_i$ path is no more than $d_i$ for $1 \le i \le p$. This problem is NP-hard even when the topology of the multicast tree is fixed. In this paper we show that every multicast tree has an underlying Steiner topology and that every minimum cost delay-constrained multicast tree corresponds to a minimum cost delay-constrained realization of a corresponding Steiner topology. We present a fully polynomial time approximation scheme for computing a minimum cost delay-constrained multicast tree under a Steiner topology. We also present computational results of a preliminary implementation to illustrate the effectiveness of our algorithm and discuss its applications.     

Distributed reformation of core-based group-shared multicast trees in mobile ad hoc networks

This paper proposes a method to reduce the cost of a core-based group-shared multicast tree, where the cost is evaluated by the total bandwidth consumption of multicasting packets among all group members. Due to the broadcast nature of radio transmissions, we find that the challenge of determining minimum cost multicast tree can be approximated by finding the multicast tree with a minimum number of non-leaves (the minimum non-leaf multicast tree problem). However, we also find that the minimum non-leaf multicast tree problem is NP-complete. Thus, a method is proposed to dynamically reduce the number of non-leaves in an existing multicast tree. Experimental results show that our method reduces the cost of the multicast tree in both geometrically and randomly distributed network models and the random waypoint mobility model.     

Distributed dynamic mobile multicast

Traditional mobile multicast schemes have either high multicast tree reconfiguration cost or high packet delivery cost. The former affects service disruption time while the latter affects packet delivery delay. Although existing region-based mobile multicast schemes offer a trade-off between two costs to some extent, most of them do not determine the size of the service range, which is critical to network performance. In this paper, we propose a novel approach, called Distributed Dynamic Mobile Multicast (D²M²), to dynamically determine the optimal service range according to the mobility and service characteristics of a user. We derive an analytical model to formulate the costs of multicast tree reconfiguration and multicast packet delivery. The model is based on a Markov chain that analyzes a mobile node’s movement in a 2D mesh network. As the complexity of computing steady probability is high, we aggregate the Markov states by leveraging mobility symmetry. Simulation shows that the network performance is enhanced through D²M².     

广域网中的快速组播树生成算法

在组播树生成算法中,MPH(minimum path cost heuristic)的费用性能几乎是最好的,但它的计算时间相对较长,提出了两种新的组播树生成算法：TNS-MPH(tree-mode started minimum-cost path heuristic)和NTDS-MPH(non-tree-destination started minimum-cost path heuristic).同时提出了一种使节点平均度非常精确的随机网络产生模型。新算法的仿真结果表明,新算法用较少的费用性能恶化来换取更快的计算速度。新算法比SCTF（selective closest terminal first）算法有更好的扩展性。     

无线Mesh 网络低干扰组播

不同于无线传感器网络和移动Ad Hoc网络,无线Mesh网络中的组播主要侧重于提高吞吐量,而干扰是影响吞吐量的重要因素。在构建组播拓扑时,传统的方法主要考虑最小价值或最短路径,而通过减少干扰来提高组播性能的研究较少,且它们的干扰计算方法都采用单播的思想,并不适合于组播。例如,当n个接收节点同时从一个节点接收数据时,在组播中这n个接收节点之间不存在干扰,而在单播中认为存在干扰。因此,提出了组播冲突图来计算组播干扰,给出组播树干扰的定义。可以发现,求最小干扰组播扰树是NP完全问题,然后提出基于万有引力的启发式算法构建具有较小干扰的组播树。为了适用于多信道的情况,提出了满足不同干扰范围的多跳信道分配算法。最后,仿真结果显示,与MCM相比,所提出的算法无论是在单天线单信道还是多天线多信道下,都能取得较高的吞吐量和较低的延迟。     

Approximate bounds and expressions for the link utilization of shortest-path multicast network traffic

Multicast network traffic is information with one source node, but many destination nodes. Rather than setting up individual connections between the source node and each destination node, or broadcasting the information to the entire network, multicasting efficiently exploits link capacity by allowing the source node to transmit a small number of copies of the information to mutually-exclusive groups of destination nodes. Multicasting is an important topic in the fields of networking (video and audio conferencing, video on demand, local-area network interconnection) and computer architecture (cache coherency, multiprocessor message passing). In this paper, we derive approximate expressions for the minimum cost (in terms of link utilization) of shortest-path multicast traffic in arbitrary tree networks. Our results provide a theoretical best-case scenario for link utilization of multicast distribution in tree topologies overlaid onto arbitrary graphs. In real networks such as the Internet MBONE, multicast distribution paths are often tree-like, but contain some cycles for purposes of fault tolerance. We find that even for richly-connected graphs such as the shufflenet and the hypercube, our expression provides a good prediction of the cost (in terms of link utilization) of multicast communication. Thus, this theoretical result has two applications: (1) a lower bound on the link capacity required for multicasting in random tree topologies, and (2) an approximation of the cost of multicasting in regular LAN and MAN topologies.     

An optimal algorithm for solving the searchlight guarding problem on weighted two-terminal series-parallel graphs

In this paper, we consider a graph problem on a connected weighted undirected graph, called the searchlight guarding problem. Our problem is an extension of so-called graph searching/guarding problem by considering the time slot parameter in addition to the traditional building cost. Suppose that there is a fugitive who moves along the edges of the graph at any speed. We want to place a set of searchlights at the vertices to search the edges of the graph and capture the fugitive. It costs some building cost to place a searchlight at some vertex. The searchlight guarding problem is to allocate a set S of searchlights at the vertices such that the total costs of the vertices in S is minimized. If there is more than one set of searchlights with the minimum building cost, then find the one with the minimum searching time, that is, the time slots needed to capture the fugitive is the minimum. The problem is known to be NP-hard on weighted bipartite graphs, split graphs, and chordal graphs; and it is linear time solvable on weighted trees and interval graphs. In this paper, an algorithm is designed to solve the problem on weighted two-terminal series-parallel graphs. It works on the parsing tree structure of the given two-terminal series-parallel graph. The algorithm is divided into two phases. In the phase one, we first extract some useful properties of optimal solutions. Employing these properties, an algorithm is designed to find the set of searchlights with the minimum guarding cost and to assign the searching directions of all edges by the dynamic programming strategy. In the phase two, the searched time slots of all edges are determined by the breadth-first-search from the root of the parsing tree. The time complexities of both phases are linear. Thus, our algorithm is time optimal. Received: 12 March 1996 / 27 May 1997     

Optimal Content Location in Multicast Based Overlay Networks with Content Updates

The architecture of overlay networks should support high-performance and high-scalability at low costs. This becomes more crucial when communication, storage costs as well as service latencies grow with the exploding amounts of data exchanged and with the size and span of the overlay network. For that end, multicast methodologies can be used to deliver content from regional servers to end users, as well as for the timely and economical synchronization of content among the distributed servers. Another important architectural problem is the efficient allocation of objects to servers to minimize storage, delivery and update costs. In this work, we suggest a multicast based architecture and address the optimal allocation and replication of dynamic objects that are both consumed and updated. Our model network includes consumers which are served using multicast or unicast transmissions and media sources (that may be also consumers) which update the objects using multicast communication. General costs are associated with distribution (download) and update traffic as well as the storage of objects in the servers. Optimal object allocation algorithms for tree networks are presented with complexities of O(N) and O(N ²) in case of multicast and unicast distribution respectively. To our knowledge, the model of multicast distribution combined with multicast updates has not been analytically dealt before, despite its popularity in the industry.     

A 3.4713-approximation algorithm for the capacitated multicast tree routing problem

Given an underlying communication network represented as an edge-weighted graph G=(V,E), a source node sV, a set of destination nodes DV, and a capacity k which is a positive integer, the capacitated multicast tree routing problem asks for a minimum cost routing scheme for source s to send data to all destination nodes, under the constraint that in each routing tree at most k destination nodes are allowed to receive the data copies. The cost of the routing scheme is the sum of the costs of all individual routing trees therein. Improving on our previous approximation algorithm for the problem, we present a new algorithm which achieves a worst case performance ratio of , where ρ denotes the best known approximation ratio for the Steiner minimum tree problem. Since ρ is about 1.55 at the writing of the paper, the ratio achieved by our new algorithm is less than 3.4713. In comparison, the previously best ratio was .     

时延及时延抖动限制的最小代价多播路由策略

满足多种服务质量请求的多播路由问题是目前多播通信中的重要课题之一。该文作者在研究受端到端时延及时延抖动限制的多播路由问题的过程中，发现当前许多算法所普遍使用的两个最佳链路选择函数并不能完全体现路由的动态过程，同时它们还存在一定的缺陷。而正是由于这种缺陷，在某些情况下通过这两个最佳链路选择函数所得到的结果树可能不包含所有的目标节点，文中称这种情况为“多播不可达”。针对上述问题，该文提出了“多播可达”的假设条件以及一个新的最佳链路选择函数，并在此基础上提出了一个满足时延及时延抖动双重限制的最小代价多播树的建立算法（DDVBMRA）以及一种动态重组多播组目标节点的方法。仿真结果表明本算法具有很好的延抖动及代价性能。     

On the Convergence of Multicast Games in Directed Networks

We investigate the convergence of the price of anarchy after a limited number of moves in the classical multicast communication game when the underlying communication network is directed. Namely, a subset of nodes of the network are interested in receiving the transmission from a given source node and can share the cost of the used links according to fixed cost sharing methods. At each step, a single receiver is allowed to modify its communication strategy, that is to select a communication path from the source, and assuming a selfish or rational behavior, it will make a best response move, that is it will select a solution yielding the minimum possible payment or shared cost. We determine lower and upper bounds on the price of anarchy, that is the highest possible ratio among the overall cost of the links used by the receivers and the minimum possible cost realizing the required communications, after a limited number of moves under the fundamental Shapley cost sharing method. In particular, assuming that the initial set of connecting paths can be arbitrary, we show an $O(r\sqrt{r})We investigate the convergence of the price of anarchy after a limited number of moves in the classical multicast communication game when the underlying communication network is directed. Namely, a subset of nodes of the network are interested in receiving the transmission from a given source node and can share the cost of the used links according to fixed cost sharing methods. At each step, a single receiver is allowed to modify its communication strategy, that is to select a communication path from the source, and assuming a selfish or rational behavior, it will make a best response move, that is it will select a solution yielding the minimum possible payment or shared cost. We determine lower and upper bounds on the price of anarchy, that is the highest possible ratio among the overall cost of the links used by the receivers and the minimum possible cost realizing the required communications, after a limited number of moves under the fundamental Shapley cost sharing method. In particular, assuming that the initial set of connecting paths can be arbitrary, we show an O(r?r)O(r\sqrt{r}) upper bound on the price of anarchy after 2 rounds, during each of which all the receivers move exactly once, and a matching lower bound, that we also extend to W(r^k?{r})\Omega(r\sqrt[k]{r}) for any number k≥2 rounds, where r is the number of receivers. Similarly, exactly matching upper and lower bounds equal to r are determined for any number of rounds when starting from the empty state in which no path has been selected. Analogous results are obtained also with respect to other three natural cost sharing methods considered in the literature, that is the egalitarian, path-proportional and egalitarian-path proportional ones. Most results are also extended to the undirected case in which the communication links are bidirectional.     

结合集中式与分布式特征的多路径QoS组播路由协议

提出了一个结合集中式算法与分布式算法优点的多路径启发式QoS组播路由算法和协议,它以单播路由协议OSPF传播链路的代价信息为基础,运用最小代价Dijkstra算法计算端节点到当前在树节点的最小代价路径,然后启动一个分布式计算过程得到一个可选路径集,加入节点通过一个综合性启发式选择其中的最佳路径连接到组播树．算法能够有效地支持延时和带宽受限的代价优化组播树构造,具有无环选路、呼叫接收成功率高、呼叫建立时间短、伸缩性好等特点．     

面向输电线故障信息传输的多播路由

针对无线传感器网络应用于输电线路故障传输时存在通信代价高、实时性差的问题,提出一种输电线路故障传输多播路由算法(MRFT)。抽象出输电线路故障信息传输网络模型;根据时延最短路径树(SPT)的最大端到端时延确定多播树时延上限,将时延上限边接入多播树;设计最小代价启发函数将剩余叶子节点接入多播树。仿真结果表明,与KPP算法相比,MRFT算法构造的多播树在多播树时延、端到端时延方差和多播树代价3个方面均有良好表现。该算法能够有效保证输电线路故障信息传输的实时性,降低通信代价。     

An artificial bee colony algorithm for the minimum routing cost spanning tree problem

Given a connected, weighted, and undirected graph, the minimum routing cost spanning tree problem seeks a spanning tree of minimum routing cost on this graph, where routing cost of a spanning tree is defined as the sum of the costs of the paths connecting all possible pairs of distinct vertices in that spanning tree. This problem has several important applications in networks design and computational biology. In this paper, we have proposed an artificial bee colony (ABC) algorithm-based approach for this problem. We have compared our approach against four best methods reported in the literature—two genetic algorithms, a stochastic hill climber and a perturbation-based local search. Computational results show the superiority of our ABC approach over other approaches.     

Approximation Algorithms for Degree-Constrained Minimum-Cost Network-Design Problems

We study network-design problems with two different design objectives: the total cost of the edges and nodes in the network and the maximum degree of any node in the network. A prototypical example is the degree-constrained node-weighted Steiner tree problem: We are given an undirected graph G(V,E) , with a nonnegative integral function d that specifies an upper bound d(v) on the degree of each vertex v ∈ V in the Steiner tree to be constructed, nonnegative costs on the nodes, and a subset of k nodes called terminals. The goal is to construct a Steiner tree T containing all the terminals such that the degree of any node v in T is at most the specified upper bound d(v) and the total cost of the nodes in T is minimum. Our main result is a bicriteria approximation algorithm whose output is approximate in terms of both the degree and cost criteria—the degree of any node v ∈ V in the output Steiner tree is O(d(v) log k) and the cost of the tree is O(log k) times that of a minimum-cost Steiner tree that obeys the degree bound d(v) for each node v . Our result extends to the more general problem of constructing one-connected networks such as generalized Steiner forests. We also consider the special case in which the edge costs obey the triangle inequality and present simple approximation algorithms with better performance guarantees. Received December 21, 1998; revised September 24, 1999.     

基于遗传算法的一种组播路由算法

在计算机通信中，越来越多的多媒体应用如视频会议、多媒体教学系统、视频点播等需要组播技术，这就需要研究如何构造有效组播树的问题。首先给出基于受限时延的最小代价组播树问题的网络模型及其数学描述。然后提出了一种采用启发式算法和遗传算法的混合算法来解决该问题。该方法可以在满足时延约束的情况下，寻找费用最小的组播路由树。数值仿真实验结果表明该算法有较好的性能，快速有效。     

Fast reroute from single link and single node failures for IP multicast

The rise in multicast implementations has seen with it an increased support for fast failure recovery from link and node failures. Most recovery mechanisms augment additional services to existing protocols causing excessive overhead, and these modifications are predominantly protocol-specific. In this paper, we develop a multicast failure recovery mechanism that constructs protocol independent fast reroute paths to recover from single link and single node failures. We observe that single link failure recovery in multicast networks is similar to recovering unicast traffic, and we use existing unicast recovery mechanisms for multicast traffic. We construct multicast protection trees that provide instantaneous failure recovery from single node failures. For a given node x, the multicast protection tree spans all its neighbors and does not include itself. Thus, when the node fails, the neighbors of the node are connected through the multicast protection tree instead of node x, and forward the traffic over the multicast protection tree for the duration of failure recovery. The multicast protection trees are constructed a priori, without the knowledge of the multicast traffic in the network. Based on simulations on three realistic network topologies, we observe that the multicast protection trees increase the routing table size only by 38% on average and the path length between any source–destination pair by 13% on average.