Deadlock-Free Multicasting in Irregular Networks Using Prefix Routing

A deadlock-free multicast scheme called prefix multicasting in irregular networks (i.e., networks with irregular topology) is studied. In prefix routing, a compact routing table is associated with each node (processor). Basically, each outgoing channel of a node is assigned a special label and an outgoing channel is selected if its label is a prefix of the label of the destination node. Node and channel labelling in an irregular network is based on a pre-defined spanning tree which may or may not be minimum. The routing process follows a two-phase process of going up and then down along the spanning tree, with a possible cross channel between two branches of the tree between two phases. It is shown that the proposed routing scheme is deadlock- and livelock-free. The approach is extended to multicasting in which the multicast packet is first forwarded up the tree to the longest common prefix (LCP) of destinations in the multicast. The packet is then treated as a multi-head worm that can split at branches of the spanning tree as the packet is sent down the tree.     

Architectural support for efficient multicasting in irregularnetworks

Parallel computing on networks of workstations is fast becoming a cost-effective high-performance computing alternative to MPPs. Such a computing environment typically consists of processing nodes interconnected through a switch-based irregular network. Many of the problems that were solved for regular networks have to be solved anew for these systems. One such problem is that of efficient multicast communication. In this paper, we propose two broad categories of schemes for efficient multicasting in such irregular networks: network interface-based (NI-based) and switch-based. The NI-based multicasting schemes use the network interface of intermediate destinations for absorbing and retransmitting messages to other destinations in the multicast tree. In contrast, the switch-based multicasting schemes use hardware support for packet replication at the switches of the network and a concept known as multidestination routing to convey a multicast message from one source to multiple destinations. We first present alternative schemes for efficient multipacket forwarding at the NI and derive an optimal k-binomial multicast tree for multipacket NI-based multicast. We then propose two switch-based multicasting schemes that differ in the power of the encoding scheme and the complexity of the decoding logic at the switches. These multicasting schemes use path-based multidestination worms that can cover all nodes connected to switches along a valid unicast path and tree-based multidestination worms that can cover entire destination sets in a single phase using one worm, respectively. For each scheme, we describe the associated header encoding and decoding operation, the method for deriving multidestination worms that cover arbitrary multicast destination sets, and the multicasting scheme using the derived multidestination worms     

基三分层网络中的受限多播路由算法

多播路由算法对互连网络的通信性能和多处理机系统性能的发挥起着重要作用。针对基三分层互连网络，在权衡性能、成本和实现的基础上，提出一种基于树的受限多播路由算法TRMA。该算法充分利用基三分层互连网络的层次特性和节点编码中所含的网络拓扑信息实现消息路由，算法设计简单，易于硬件实现。和其他基于树的多播路由算法相比，TRMA算法不需要源节点在发送消息前构建多播树,并将多播树的信息存放在消息中，大大降低了源节点的工作负载，提高整个系统的性能。通过仿真比较了TRMA和基于单播的多播路由算法，结果表明TRMA具有较低的网络延迟和较小的网络流量。     

A theory of deadlock-free adaptive multicast routing in wormholenetworks

A theory for the design of deadlock-free adaptive routing algorithms for wormhole networks, proposed by the author (1991, 1993), supplies sufficient conditions for an adaptive routing algorithm to be deadlock-free, even when there are cyclic dependencies between channels. Also, two design methodologies were proposed. Multicast communication refers to the delivery of the same message from one source node to an arbitrary number of destination nodes. A tree-like routing scheme is not suitable for hardware-supported multicast in wormhole networks because it produces many headers for each message, drastically increasing the probability of a message being blocked. A path-based multicast routing model was proposed by Lin and Ni (1991) for multicomputers with 2D-mesh and hypercube topologies. In this model, messages are not replicated at intermediate nodes. This paper develops the theoretical background for the design of deadlock-free adaptive multicast routing algorithms. This theory is valid for wormhole networks using the path-based routing model. It is also valid when messages with a single destination and multiple destinations are mixed together. The new channel dependencies produced by messages with several destinations are studied. Also, two theorems are proposed, developing conditions to verify that an adaptive multicast routing algorithm is deadlock-free, even when there are cyclic dependencies between channels. As an example, the multicast routing algorithms of Lin and Ni are extended, so that they can take advantage of the alternative paths offered by the network     

一种基于网络分解的多播通讯路由方法

有效的消息通讯是提高分布存储器并行计算机性能的关键因素．点对点通讯和广播通讯是２种常用的消息通讯方法，而多播通讯（Ｍｕｌｔｉｃａｓｔｉｎｇ）是指从一个源节点同时给任意多个目标节点发送消息，这种通讯比点对点和广播２种方式更具一般性，适用于很多实际应用的需求．本文针对ＰＡＲ９５并行计算机的二维网格结构，提出一种基于网络分解的多播消息通讯方法，并比较了该方法与用多个点对点方法实现多播通讯的性能.     

Unicast-based multicast communication in wormhole-routed networks

Multicast communication, in which the same message is delivered from a source node to an arbitrary number of destination nodes, is being increasingly demanded in parallel computing. System supported multicast services can potentially offer improved performance, increased functionality, and simplified programming, and may in turn be used to support various higher-level operations for data movement and global process control. This paper presents efficient algorithms to implement multicast communication in wormhole-routed direct networks, in the absence of hardware multicast support, by exploiting the properties of the switching technology. Minimum-time multicast algorithms are presented for n-dimensional meshes and hypercubes that use deterministic, dimension-ordered routing of unicast messages. Both algorithms can deliver a multicast message to m-1 destinations in [log ₂ m] message passing steps, while avoiding contention among the constituent unicast messages. Performance results of implementations on a 64-node nCUBE-2 hypercube and a 168-node Symult 2010 2-D mesh are given     

Adaptive Fault-Tolerant Multicast in Hypercube Multicomputers

Fault-tolerant message routing mechanism is a key to the performance of reliable multicomputers. Multicast refers to the delivery of the same message from a source node to an arbitrary number of destination nodes. This paper presents two types of partially adaptive fault tolerant multicast algorithms. The Type A algorithm can deliver messages to all destinations through shortest paths if each fault-free node has at most one faulty neighbor. The Type B algorithm can deliver messages to all destinations if the total number of faulty links and faulty nodes is less than the dimension of the hypercube. The proposed algorithms have the following important features: they are distributed, they only require local information to determine the paths, and they need very little additional message overhead. The performance of the algorithms, measured by the traffic created by the communication, is very close to that in fault-free hypercubes.     

Efficient path-based multicast in wormhole-routed mesh networks

The capability of multidestination wormhole allows a message to be propagated along any valid path in a wormhole-routed network conforming to the underlying base routing scheme. The multicast on the path-based routing model is highly dependent on the spatial locality of destinations participating in multicasting. In this paper, we propose two proximity grouping schemes for efficient multicast in wormhole-routed mesh networks with multidestination capability by exploiting the spatial locality of the destination set. The first grouping scheme, graph-based proximity grouping, is proposed to group the destinations together with locality to construct several disjoint sub-meshes. This is achieved by modeling the proximity grouping problem to graph partitioning problem. The second one, pattern-based proximity grouping, is proposed by the pattern classification schemes to achieve the goal of the proximity grouping. By simulation results, we show the routing performance gains over the traditional Hamiltonian-path routing scheme.     

多媒体通信中带度约束的多播路由算法

随着多媒体业务的发展,多播技术应用日益广泛,多播路由是要寻找连接源节点和一组目的节点的一棵多播树,这个问题在数学上归结为Steiner树问题,它是一个NPC问题。在实际网络中,网络节点具备不同的多播能力,有些节点不支持多播,有些节点支持多播,但为了保证网络速度和节点负载平衡,支持多播的节点要限制其复制信息的数量,即节点的多播能力受限。在这种情况下,寻找多播树变得更加困难,该文用节点的约束来表示敏个节点具备的多播能力,节点多播能力受限情况下的多播路由问题被称为带度约束的多播路由问题,其仍是一个NPC问题。该文提出了一种求解带度的约束多播路由问题的双层遗传算法。算法的基本思想是最优多播树应是一棵满足度约束的最小生成树,因此问题的关键在于如何找到包括在最优生成树中的Steiner节点。遗传算法 采用二进制编码方式,内层算法用于求解满足度约束的最小生成树;外层算法进行全局搜索。该文将算法在稀疏图上进行实验,为了更好地模拟真实网络,稀疏图中每个节点具有不同的多播能力,并且多播目的节点数目相比于网络节点数要小。实验对算法进行了三方面比较：（1）解的质量;（2）计算时间;（3）算法的收敛性。实验结果表明,文中提出的遗传算法能够找到费用较小的多播树,但是当网络规模增大时,算法的求解时间也较长。     

Turn Grouping for Multicast in Wormhole-Routed Mesh Networks Supporting the Turn Model

Multicast is an important collective communication in scalable parallel computers. One efficient scheme to perform multicast is multidestination messaging[8]. In multidestination messaging, destination nodes of a multicast are partitioned into disjoint groups. Nodes in each group are reached with a multidestination message that conforms to the base routing algorithm of the system. A systematic way of partitioning the nodes is critical to the efficiency of multidestination messaging. In this paper we propose a node grouping method, called turn grouping, for partitioning the destination nodes in a multicast. Turn grouping is general in the sense that it supports any base routing algorithm derivable from the turn model [5]. Given such a base routing algorithm and the corresponding prohibited turns, turn grouping can systematically produce a proper schedule for multicasting the message. We evaluated the performance of turn grouping using three typical turn model-based routing algorithms. The simulation results show that our approach performs better than the Umesh [12] and the Hamiltonian-path [8] algorithms.     

Reliable Communication on Cube-Based Multicomputers

We consider a distributed unicasting algorithm for hypercubes with faulty nodes(including disconnected hypercubes)using the safety level concept.The safety level of ach node in an n-dimensional hypercube in an approximated measure of the number and distribution of faulty nodes in the neighborhood and it can be easily calculated through n-1 rounds of information exchange among neighboring nodes.Optimal unicasting between two nodes is guaranteed if the safety level of the source node is no less than the Hamming distance between the source and the destination.The feasibility of an optimal or suboptimal unicasting can be easily determined at the source node by comparing its safety level,together with its neighbors‘ safety levels,with the Hamming distance between the source and the destination.The proposed scheme is also the first attempt to address the unicasting problem in discronnected hypercubes.The safety level concept is also extended to be used in hypercubes with both faulty nodes and links and in generalized hypercubes.     

Routing in modular fault-tolerant multiprocessor systems

In this paper, we consider a class of modular multiprocessor architectures in which spares are added to each module to cover for faulty nodes within that module, thus forming a fault-tolerant basic block (FTBB). In contrast to reconfiguration techniques that preserve the physical adjacency between active nodes in the system, our goal is to preserve the logical adjacency between active nodes by means of a routing algorithm which delivers messages successfully to their destinations. We introduce two-phase routing strategies that route messages first to their destination FTBB, and then to the destination nodes within the destination FTBB. Such a strategy may be applied to a variety of architectures including binary hypercubes and three-dimensional tori. In the presence of f faults in hypercubes and tori, we show that the worst case length of the message route is min {σ+f, (K+1)σ}+c where σ is the shortest path in the absence of faults, K is the number of spare nodes in an FTBB, and c is a small constant. The average routing overhead is much lower than the worst case overhead     

Near-optimal broadcast in all-port wormhole-routed hypercubes usingerror-correcting codes

A new broadcasting method is presented for hypercubes with wormhole routing mechanism. The communication model assumed allows an n-dimensional hypercube to have at most n concurrent 110 communications along its ports. It further assumes a distance insensitivity of (n+1) with no intermediate reception capability for the nodes along the communication path. The approach is based on determination of the set of nodes (called stations) in the hypercube such that for any node in the network there is a station at distance of at most 1. Once stations are identified, parallel disjoint paths are formed from the source to all stations. The broadcasting is accomplished first by sending the message to all stations which will in turn inform the rest of the nodes of the message. To establish node-disjoint paths between the source node and all stations, we introduce a new routing strategy. We prove that multicasting can be done in one routing step as long as the number of destination nodes are at most n in an n-dimensional hypercube. The number of broadcasting steps using our routing is equal to or smaller than that obtained in an earlier work; this number is optimal for all hypercube dimensions n⩽12, except for n=10     

Performance comparison of different multicast routing strategies in disruption tolerant networks

Disruption Tolerant Networks (DTNs) technologies are emerging solutions to networks that experience frequent partitions. As a result, multicast design in DTNs is a considerably more difficult problem compared to that in Internet and mobile ad hoc networks. In this paper, we first investigate three basic DTN multicast strategies, including unicast-based multicast (U-Multicast), static-tree-based multicast (ST-Multicast) and dynamic-tree-based multicast (DT-Multicast) strategies. Then we focus on studying two DT-Multicast routing schemes: Dynamic Tree Based Routing (DTBR) and On-demand Situation-aware Multicast (OS-Multicast), which address the challenges of utilizing opportunistic links to conduct dynamic multicast structures in DTNs. Performances of different strategies are then evaluated by simulations, including applying the real-world DTN traces. Our results show that OS-Multicast and DTBR can achieve higher message delivery ratio than that of using U-Multicast and ST-Multicast strategies. Also, to get better performance, we recommend that system designers select OS-Multicast when the source traffic rate is low.     

Multipath-Based Multicasting Strategies for Wormhole-Routed Star Graph Interconnection Networks

The star graph interconnection network has been recognized as an attractive alternative to the popular hypercube network. In this paper, we present a multipath-based multicast routing model for wormholerouted star graph networks, propose two efficient multipath routing schemes, and contrast the performance of the proposed schemes with the performance of the scheme presented in our previous work. Both of the two proposed schemes have been proven to be deadlock-free. The first scheme, simple multipath routing, uses multiple independent paths for concurrent multicasting. The second scheme, two-phase multipath routing, includes two phases: source-to-relay and relay-to-destination. For each phase, multicasting is carried out using simple multipath routing. Experimental results show that, for short and medium messages with small message startup latencies, the proposed schemes reduce multicast latency more efficiently than other schemes.     

Deadlock-free multicast wormhole routing in 2-D mesh multicomputers

Multicast communication services, in which the same message is delivered from a source node to an arbitrary number of destination nodes, are being provided in new-generation multicomputers. Broadcast is a special case of multicast in which a message is delivered to all nodes in the network. The nCUBE-2, a wormhole-routed hypercube multicomputer, provides hardware support for broadcast and a restricted form of multicast in which the destinations form a subcube. However, the broadcast routing algorithm adopted in the nCUBE-2 is not deadlock-free. In this paper, four multicast wormhole routing strategies for 2-D mesh multicomputers are proposed and studied. All of the algorithms are shown to be deadlock-free. These are the first deadlock-free multicast wormhole routing algorithms ever proposed. A simulation study has been conducted that compares the performance of these multicast algorithms under dynamic network traffic conditions in a 2-D mesh. The results indicate that a dual-path routing algorithm offers performance advantages over tree-based, multipath, and fixed-path algorithms     

Fault-tolerant multicasting in hypercubes using local safety information

A fully unsafe hypercube according to the global safety can be split into a unique set of maximal safe subcubes. Multicasting in a maximal safe subcube can be completed reliably based on information related to the maximal safe subcube. A time-optimal multicasting exists if (1) the multicast source is locally safe in the minimum subcube that contains the source and destinations (called a multicast subcube), or (2) the spanning subcube between each destination and the source is safe. We show a sufficient condition for the existence of a multicasting is: the multicast subcube is safe or the spanning subcube between the source and each destination is either safe or is contained in a safe subcube. Methods are presented to set up a partial multicast tree when the above sufficient conditions fail. It is shown that effectiveness of the algorithm can be improved drastically using the partial multicast tree setup technique. Extensive simulation results are also presented.     

A hardware supported multicast scheme based on XY routing for 2-D mesh InfiniBand networks

The multicast operation is a useful operation in parallel applications. It is therefore important to ensure that for a given architecture, the parallel application runs efficiently. With the hardware-supported multicast of the InfiniBand Architecture (IBA), we propose a multicast scheme for m×n mesh InfiniBand networks based on XY routing. The basic concept of the proposed multicast scheme is to find the union sets of the output ports of switches, which are in the paths between the source node and each destination node in a multicast group. Furthermore, in the proposed scheme, we consider the usage of virtual lanes and evaluate their performance. We implement the proposed multicast scheme on a 2-D mesh InfiniBand network simulator. Several multicast configurations consisting of different message size, different traffic workload and different number of virtual lanes are simulated. The simulation results show that the proposed multicast scheme outperforms its corresponding unicast scheme for all simulation cases. The larger the message size, the larger the number of multicast source nodes, and the larger the size of the multicast group, the better the speedup that can be expected from the proposed multicast scheme. The usage of virtual lanes is also shown to improve the speed of the multicast operations.     

An Efficient Tree-Based Multicasting Algorithm on Wormhole-Routed Star Graph Interconnection Networks Embedded with Hamiltonian Path

Multicasting is an important issue for numerous applications in parallel and distributed computing. In multicasting, the same message is delivered from a source node to an arbitrary number of destination nodes. The star graph interconnection network has been recognized as an attractive alternative to the popular hypercube network. In this paper, we propose an efficient and deadlock-free tree-based multi-cast routing scheme for wormhole-routed star graph networks with hamiltonian path. In our proposed routing scheme, the router is with the input-buffer-based asynchronous replication mechanism that requires extra hardware cost. Meanwhile, the router simultaneously sends incoming flits on more than one outgoing channel. We perform simulation experiments with the network latency and the network traffic. Experimental results show that the proposed scheme reduces multicast latency more efficiently than other schemes.     

Some permutation routing algorithms for low-dimensional hypercubes

Oblivious permutation routing in binary d-cubes has been well studied in the literature. In a permutation routing, each node initially contains a packet with a destination such that all the 2^d destinations are distinct. Kaklamanis et al. (Math. Syst. Theory 24 (1991) 223–232) used the decomposability of hypercubes into Hamiltonian circuits to give an asymptotically optimal routing algorithm. The notion of “destination graph” was first introduced by Borodin and Hopcroft to derive lower bounds on routing algorithms. This idea was recently used by Grammatikakis et al. (Proceedings of the Advancement in Parallel Computing, Elsevier, Amsterdam, 1993) to construct many–one routing algorithms for the binary 2-cube and 3-cube. In the present paper, further theoretical development is made along this line. It is then applied to obtain algorithms for binary d-cubes with d up to 12, which compare favorably with the above-mentioned “Hamiltonian circuit” algorithm. Some results on t-nary cubes with t3 are also obtained.