Efficient multicast schemes for 3-D Networks-on-Chip

3-D Networks-on-Chip (NoCs) have been proposed as a potent solution to address both the interconnection and design complexity problems facing future System-on-Chip (SoC) designs. In this paper, two topology-aware multicast routing algorithms, Multicasting XYZ (MXYZ) and Alternative XYZ (AL + XYZ) algorithms in supporting of 3-D NoC are proposed. In essence, MXYZ is a simple dimension order multicast routing algorithm that targets 3-D NoC systems built upon regular topologies. To support multicast routing in irregular regions, AL + XYZ can be applied, where an alternative output channel is sought to forward/replicate the packets whenever the output channel determined by MXYZ is not available. To evaluate the performance of MXYZ and AL + XYZ, extensive experiments have been conducted by comparing MXYZ and AL + XYZ against a path-based multicast routing algorithm and an irregular region oriented multiple unicast routing algorithm, respectively. The experimental results confirm that the proposed MXYZ and AL + XYZ schemes, respectively, have lower latency and power consumption than the other two routing algorithms, meriting the two proposed algorithms to be more suitable for supporting multicasting in 3-D NoC systems. In addition, the hardware implementation cost of AL + XYZ is shown to be quite modest.     

Approximation Algorithms for a Capacitated Network Design Problem

We study a capacitated network design problem with applications in local access network design. Given a network, the problem is to route flow from several sources to a sink and to install capacity on the edges to support the flow at minimum cost. Capacity can be purchased only in multiples of a fixed quantity. All the flow from a source must be routed in a single path to the sink. This NP-hard problem generalizes the Steiner tree problem and also more effectively models the applications traditionally formulated as capacitated tree problems. We present an approximation algorithm with performance ratio (_ST + 2) where _ST is the performance ratio of any approximation algorithm for the minimum Steiner tree problem. When all sources have unit demand, the ratio improves to _ST + 1) and, in particular, to 2 when all nodes in the graph are sources.     

Approximation Algorithms for a Capacitated Network Design Problem

We study a capacitated network design problem with applications in local access network design. Given a network, the problem is to route flow from several sources to a sink and to install capacity on the edges to support the flow at minimum cost. Capacity can be purchased only in multiples of a fixed quantity. All the flow from a source must be routed in a single path to the sink. This NP-hard problem generalizes the Steiner tree problem and also more effectively models the applications traditionally formulated as capacitated tree problems. We present an approximation algorithm with performance ratio (ρ_ST + 2) where ρ_ST is the performance ratio of any approximation algorithm for the minimum Steiner tree problem. When all sources have unit demand, the ratio improves to ρ_ST + 1) and, in particular, to 2 when all nodes in the graph are sources.     

一种有效的时延约束组播路由算法

在多媒体通信网络中,组播问题提出了新的要求,除了最小化组播通信的代价,同时要求保证每一个目的的节点在固定的延时之内接收信息,在这篇论文中,我们提出了一个边路选择函数用于解决时延约束组播问题,我们的实验结果揭示了该函数能提供满足时约束且代价较小的组播路由问题近似解。     

Scheduling time-constrained multicast messages in circuit-switched tree networks

In this paper, we consider a kind of multicast scheduling problem in a tree network. Each multicast message is transmitted through a directed subtree within the tree network. The transmission time of each multicast message is assumed to be one unit. Two messages can be transmitted at the same time if their subtrees are edge-disjoint. Each message is constrained by a ready time and a deadline, and has a weight we can gain if it is scheduled within its deadline. The optimality criterion is the total weight we gain. We assume that the degree of each subtree is bounded by a constant d and present an approximation algorithm of which the approximation ratio is at most 4d+15.     

Improving routing distance for geographic multicast with Fermat points in mobile ad hoc networks

In mobile ad hoc networks (MANETs), each node has the ability to transmit, receive, and route packets, and also moves through the field either randomly or in accordance with a pre-planned route. For enhancing the performance of MANETs, reducing the routing distance is a primary concern. For either ad hoc or static networks, the problem of minimizing the overall routing distance during multicasting is NP-complete. Therefore, it is difficult to determine an optimal solution. This paper presents an efficient geographic multicast protocol, designated as GMFP, based on the use of Fermat points. The objective of GMFP is to improve the overall routing distance for multicast tasks. Through a series of simulations, it is shown that GMFP outperforms the conventional Position-Based Multicast protocol and FERMA protocol in terms of the total routing distance, the packet transmission delay, the packet delivery ratio, and the node energy consumption. The performance improvements provided by GMFP are apparent as the scale of the network topology increases.     

Routing of multicast audio/video streams in reconfigurable WDM optical networks

Due to its low attenuation, fiber has become the medium of choice for point-to-point links. Using Wavelength-Division Multiplexing (WDM), many independent channels can be created in the same fiber. A network node equipped with a tunable optical transmitter can select any of these channels for sending data. An optical interconnection combines the signal from the various transmitters in the network, and makes it available to the optical receivers, which may also be tunable. By properly tuning transmitters and/or receivers, point-to-point links can be dynamically created and destroyed. Therefore, in a WDM network, the routing algorithm has an additional degree of freedom compared to traditional networks: it can modify the netowrk topology to create the routes. In this paper, we consider the problem of routing multicast audio/video streams in WDM networks and propose heuristic algorithms to solve it. The performance of these heuristics is evaluated in a number of scenarios, with a realistic traffic model, and from the evaluation we derive guidelines for usage of the proposed algorithms.This work was supported in part by NASA under grant NAG2-842, by the National Science Foundation under grant NCR-9016032 and by Pacific Bell. Ciro Noronha was supported by a graduate scholarship from FAPESP from Sept/89 to Aug/93 under grant 89/1658.     

1.5-Approximation algorithm for weighted maximum routing and wavelength assignment on rings

We give a 1.5-approximation algorithm for the weighted maximum routing and wavelength assignment problem on undirected ring networks. This improves the previous 1.58-approximation result.     

基于遗传算法的QoS多播路由优化算法

研究了带宽、延时、延时抖动和分组丢失率约束以及费用最小的QoS多播路由优化问题,提出了一种启发式遗传算法、该算法采用可变长度染色体(路由串)和它的基因(节点)应用于编码问题。交叉操作在交叉点进行部分染色体(部分路由)交换,变异操作维持种群的多样性。该算法采用简单维护操作维护好所有的不可行的染色体,交叉操作和变异操作相结合保证了最优解的搜索能力和解的全局收敛性。计算机仿真实验证明该算法快速有效,可靠性高。     

An iterative local search approach based on fitness landscapes analysis for the delay-constrained multicast routing problem

This paper presents the first fitness landscape analysis on the delay-constrained least-cost multicast routing problem (DCLC-MRP). Although the problem has attracted an increasing research attention over the past decade in telecommunications and operational research, little research has been conducted to analyze the features of its underlying landscape. Two of the most commonly used landscape analysis techniques, the fitness distance correlation analysis and the autocorrelation analysis, have been applied to analyze the global and local landscape features of DCLC-MRPs. A large amount of simulation experiments on a set of problem instances generated based on the benchmark Steiner tree problems in the OR-library reveals that the landscape of the DCLC-MRP is highly instance dependent with different landscape features. Different delay bounds also affect the distribution of solutions in the search space. The autocorrelation analysis on the benchmark instances of different sizes and delay bounds shows the impact of different local search heuristics and neighborhood structures on the fitness distance landscapes of the DCLC-MRP. The delay bound constraint in the DCLC-MRP has shown a great influence on the underlying landscape characteristic of the problem. Based on the fitness landscape analysis, an iterative local search (ILS) approach is proposed in this paper for the first time to tackle the DCLC-MRP. Computational results demonstrate the effectiveness of the proposed ILS algorithm for the problem in comparison with other algorithms in the literature.     

Scheduling and performance analysis of multicast interconnects

Multicast is an important operation in various emerging computing/networking applications. In particular, many multicast applications require not only multicast capability but also predictable communication performance, such as guaranteed multicast latency and bandwidth, called quality-of-service (QoS). In this paper, we consider scheduling in multicast interconnects, which aims to minimize the multicast latency for a set of multicast requests. Unfortunately, such a problem has been proved to be NP-Complete, which means that it is unlikely to find a fast exact algorithm for the multicast scheduling problem. We then turn to propose a simple, fast greedy multicast scheduling algorithm and derive a lower bound and an upper bound on the performance of the algorithm. As can be seen, while a lower bound is fairly straightforward, the upper bound is much more difficult to obtain. By translating the multicast scheduling problem into a graph theory problem and employing a random graph approach, we are able to obtain a probabilistic upper bound on the performance of the multicast scheduling algorithm. Our analytical and simulation results show that the performance of the proposed multicast scheduling algorithm is quite close to the lower bound and is statistically guaranteed by the probabilistic upper bound. The research work was supported in part by the U.S. National Science Foundation under grant numbers CCR-0073085 and CCR-0207999.     

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.     

Fat-tree routing and node ordering providing contention free traffic for MPI global collectives

As the size of High Performance Computing clusters grows, so does the probability of interconnect hot spots that degrade the latency and effective bandwidth the network provides. This paper presents a solution to this scalability problem for real life constant bisectional-bandwidth fat-tree topologies. It is shown that maximal bandwidth and cut-through latency can be achieved for MPI global collective traffic. To form such a congestion-free configuration, MPI programs should utilize collective communication, MPI-node-order should be topology aware, and the packet routing should match the MPI communication patterns. First, we show that MPI collectives can be classified into unidirectional and bidirectional shifts. Using this property, we propose a scheme for congestion-free routing of the global collectives in fully and partially populated fat trees running a single job. The no-contention result is then obtained for multiple jobs running on the same fat-tree by applying some job size and placement restrictions. Simulation results of the proposed routing, MPI-node-order and communication patterns show no contention which provides a 40% throughput improvement over previously published results for all-to-all collectives.     

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.     

An efficient algorithm for group multicast routing with bandwidth reservation

Multicasting refers to the transmission of data from a source node to multiple destination nodes in a network. Group multicasting is a generalisation of multicasting whereby every member of a group is allowed to multicast messages to other members that belong to the same group. The routing problem in this case involves the construction of a set of low cost multicast trees with bandwidth requirements, one for each member of the group, for multicasting messages to other members of the group. In this paper, we propose a new heuristic algorithm to generate a set of low cost multicast trees with bandwidth requirements. Simulation results show that our proposed algorithm performed better in terms of cost and in terms of utilisation of bandwidth as compared to an existing algorithm that was proposed by Jia and Wang [3].     

Algorithms for delay-constrained low-cost multicast tree construction

With the proliferation of multimedia group applications, the construction of multicast trees satisfying quality of service (QoS) requirements is becoming a problem of prime importance. Multicast groups are usually classified as sparse or pervasive groups depending on the physical distribution of group members. They are also classified based on the temporal characteristics of group membership into static and dynamic groups. In this paper, we propose two algorithms for constructing multicast trees for multimedia group communication in which the members are sparse and static. The proposed algorithms use a constrained distributed unicast routing algorithm for generating low-cost, bandwidth and delay constrained multicast trees. These algorithms have lower message complexity and call setup time due to their nature of iteratively adding paths, rather than edges, to partially constructed trees. We study the performance (in terms of call acceptance rate, call setup time and multicast tree cost) of these algorithms through simulation by comparing them with that of a recently proposed algorithm (V. Kompella, J.C. Pasquale, G.C. Polyzos, Two distributed algorithms for the constrained Steiner tree problem, in: Proc. Comp. Comm. Networking, San Diego, CA, June 1993) for the same problem. The simulation results indicate that the proposed algorithms provide larger call acceptance rates, lower setup times and comparable tree costs.     

A new approach for delay-constrained routing

Delay-constrained routing protocols are used to find paths subject to a delay constraint while efficiently using network resources. Many of the delay-constrained routing protocols that have been proposed in the literature give priority to cost minimization during the path computing process. With this approach, paths with end-to-end delays too close to the delay constraint are obtained. We believe that such paths are prone to delay constraint violations during load variations in the network. The root of such violations can be found in the imprecision of delay information during the routing process. In this paper, we propose a new approach for delay-constrained routing which captures the tradeoff between cost minimization and the risk level regarding to the delay constraint. We propose a protocol called Parameterized Delay-Constrained Routing protocol that implements our approach using a simple and efficient parameterized selection function. We expand this work to multicasting by proposing three new delay-constrained multicast routing protocols based on the source (Naïve), destination (Greedy) and mixed multicast routing techniques. Our simulations show that our protocols produce paths and trees which are stable, less risky and suitable for various network conditions.