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The problem graph for matrix algorithms analyzed in this paper is a twodimensional grid (toroidal mesh) which is mapped onto a hypercube topology.


It is shown thatNhypercube topology is a reasonable solution toimplement NN of threshold gates, in particular, on thesingleelectron devices.


The threedimensional (3D) model of a feedforward neural network(NN) based on so called Nhypercube topology isproposed.


Initially, the processors know only the size of the network and that they are interconnected in a hypercube topology.


This graph of processes is suitably mapped onto a hypercube topology so as to minimize the communication cost.

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 In this paper, star graph is introduced. Star graph has many superiortopological properties, such as vertex symmetry and edge symmetry, short diameter,regular and reliable and so on. The nStar graph, denoted by Sm, is one of thegraph networks that have been recently proposed as attractive alternatives to thetraditional hypercube topology for interconnecting processors in parallel computers.lt is known that deadlock can be prevented by routing restriction in some highlyregular networks. This paper studies... In this paper, star graph is introduced. Star graph has many superiortopological properties, such as vertex symmetry and edge symmetry, short diameter,regular and reliable and so on. The nStar graph, denoted by Sm, is one of thegraph networks that have been recently proposed as attractive alternatives to thetraditional hypercube topology for interconnecting processors in parallel computers.lt is known that deadlock can be prevented by routing restriction in some highlyregular networks. This paper studies deadlockfree behavioral routing algorithm onstar graph. First, this paper defines kdimensional matched bases in star graph,and defines a regular projection from S.(B) to Sk on the basis of the properties ofthe matched bases. Then two of the deadlockfree routing restrictions on star graphare presented. Finally, a algorithm of the deadlockfree routing restrictions isproved This paper also indicated that the minimum deadlockfree routing restrictions on star graph is an open problem.  星形图具有许多良好的拓扑性质，是一种有可能替代传统的超立方体的并行计算互联网络的模型．在本文中，作者针对在星形图这样一种高度规则的网络中，可能产生死锁的问题，对星形图上无死锁的路径算法进行了研究．首先利用星形图中匹配基的性质，给出了从Sn（B）到Sk的正规映射的定义，然后提出了星形图上的两个无死锁受限条件，最后证明了一个满足无死锁受限条件的路径算法．作者还提出了星形图上路径算法的最小无死锁受限条件等，有待于进一步研究．  Reliable and scalable multicast is an active research field of multicast in recent years. A hypercube based reliable & scalable multicast control mechanism is presented to solve the contradiction problem of multicast reliability and related scalability, which combines the hypercube geometric character of multicast reliable solution and the localization of multicast scalable solution. The mechanism is implemented by embedding the 1 dimension tree topology into n dimension hypercube topology and applying... Reliable and scalable multicast is an active research field of multicast in recent years. A hypercube based reliable & scalable multicast control mechanism is presented to solve the contradiction problem of multicast reliability and related scalability, which combines the hypercube geometric character of multicast reliable solution and the localization of multicast scalable solution. The mechanism is implemented by embedding the 1 dimension tree topology into n dimension hypercube topology and applying the local ARQ recovery to the hypercube topology. The experiments and tests are based on the MS Windows platform and 100M Ethernet LAN. According to the theory analysis and experiment results, the hypercube based reliable & scalable mechanism shows efficient reliability and high scalability (the reliablility will increase with the scalability of node numbers in the hypercube,which can achieve over 90% reliability with only 4 nodes.), which can fulfil the requirement of reliable & scalable multicast in different network environments.  针对多点组播 ( m ulticast)控制机制中可靠性 ( reliability)与可扩展性 ( scalability)间存在的问题 ,将扩展性方案中超立方体 ( hypercube)拓扑思想与可靠性方案中反馈重发局部化 ( localization)思想用于控制机制 ,提出一种基于超立方体拓扑的可靠扩展控制机制 :将组播节点控制拓扑从 1维树型拓扑映射为 n维超立方体拓扑 ,运用超立方体拓扑的几何特性将基于包丢失的局部反馈重发可靠性有效融于节点扩展性中 ,实现组播的有效可靠扩展 .理论分析与实际测试表明 :控制机制有着良好的扩展性和可靠性 ,可满足不同网络条件下的多点组播的可靠性扩展 .  Multicast video over IP, as an important application of network multimedia, is an active research field these years. One of the focuses is the reliable multicast of its control information in the scalable video nodes topology, for which multicast reliability and its scalability are not easy to be combined in the same control mechanism. This paper presents a hypercubebased multicast reliable & scalable solution, which is combined the hypercube character of scalable solution with the localization character of... Multicast video over IP, as an important application of network multimedia, is an active research field these years. One of the focuses is the reliable multicast of its control information in the scalable video nodes topology, for which multicast reliability and its scalability are not easy to be combined in the same control mechanism. This paper presents a hypercubebased multicast reliable & scalable solution, which is combined the hypercube character of scalable solution with the localization character of reliable solution to solve the problem.The solution can be described briefly in the following way: first embedding the 1dimension tree topology of multicast video nodes into Ndimension hypercube topology by the Liebeherr solution, in which some proper modifications are made for the specific Multicast video application; then using some realtime dynamic management of the hypercube topology to guarantee the mechanism in the stable hypercube state and updating the nodes topology information by multicasting control information periodically; finally keeping the latest node and neighbor node information for the reliable transmit of the multicast video control information and recovering the loss locally if finding the control information loss. In the remaining part of the paper, the reliability recovery course and performance test are discussed. In the reliability recovery course, the related analyses are based on the probability theory of packet loss, in which node receiving probability and mechanism average receiving probability are definitely formulated. For the performance test, the related test course and test result analysis are given to show the reliable & scalable performance of the mechanism, in which the nodes simulation and loss simulation of the network are implemented by using the existed methods, which feasibility are be already validated. According to the theory analysis and experiment result, the hypercubebased reliable & scalable control shows efficient reliability and highly scalability, which performs more reliability with the increase of the nodes in the hypercube topology.  针对 IP多点组播视频控制信息组播传输的可靠扩展问题 ,将组播扩展性方案超立方体 ( hypercube)拓扑思想与组播可靠性方案反馈重发局部化 ( localization)思想用于控制机制 ,提出了一种基于超立方体拓扑的可靠扩展控制机制 :将控制拓扑从 1维树型映射为 n维超立方体拓扑 ,运用超立方体结构几何特性将局部反馈重发恢复融入拓扑节点扩展中 ,实现了视频控制信息的有效可靠扩展 .理论分析与实际测试表明 :基于超立方体拓扑的控制机制有较好的可靠扩展性 .  
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