Hafizur Rahman - Academia.edu (original) (raw)
Papers by Hafizur Rahman
Applied Sciences, 2020
In order to fulfill the increasing demand for computation power to process a boundless data concu... more In order to fulfill the increasing demand for computation power to process a boundless data concurrently within a very short time or real-time in many areas such as IoT, AI, machine learning, smart grid, and big data analytics, we need exa-scale or zetta-scale computation in the near future. Thus, to have this level of computation, we need a massively parallel computer (MPC) system that shall consist of millions of nodes; and, for the interconnection of these massive numbers of nodes, conventional topologies are infeasible. Thus, a hierarchical interconnection network (HIN) is a rational way to connect huge nodes. Through this article, we are proposing a new HIN, which is a tori-connected flattened butterfly network (TFBN) for the next generation MPC system. Numerous basic modules are hierarchically interconnected as a toroidal connection, whereby the basic modules are flattened butterfly networks. We have studied the network architecture, static network performance, and static cost...
The most critical component in determining the ultimate performance potential of a multicomputer ... more The most critical component in determining the ultimate performance potential of a multicomputer is its interconnection network. In this dissertation, we propose a new hierarchical interconnection network, called the Hierarchical Torus Network (HTN) for large scale 3D multicomputers. It consists of multiple basic modules (BMs) which are 3D-tori (m × m × m) and are hierarchically interconnected by 2D-tori (n × n). Both the BMs and the interconnection at higher levels are toroidally connected, hence the name Hierarchical Torus Network (HTN). To reduce the vertical links between silicon planes, we consider higher-level networks as 2D-torus instead of 3D-torus network. We have explored various aspects such as network diameter, cost, average distance, bisection width, peak number of vertical links, and VLSI
Proceedings of the Canadian Engineering Education Association (CEEA), 2020
This paper addresses the construction of a novel approach to enhance learner motivation as it rel... more This paper addresses the construction of a novel approach to enhance learner motivation as it relates to the learning process. The foundational principles of motivation are discussed. The impact of instructional technology on student motivation through an innovative web-based problem-solving system is the main focus of this study. The development of the web-based problem-solving system and its evaluation process are considered for addressing the foundational principles of motivation. The proposed system is customizable to provide feedback to both students and instructors. The outcome of this research will help establish a suitable instructional design model of motivation for engineering students. The process also has prospects for applications in other disciplines.
Procedia Computer Science, 2015
A Symmetric Midimew Mesh connected network (SMMN) is a hierarchical interconnection networks (HIN... more A Symmetric Midimew Mesh connected network (SMMN) is a hierarchical interconnection networks (HIN) that capable to interconnect vast number of nodes that could reach up to millions of nodes in the network. SMMN has multiple basic modules of 2D-mesh networks that are recursively interconnected by Midimew network to create higher-level networks. In this paper, we explain the architectural details of SMMN ,we also present the a deadlock-free routing algorithm for SMMN using four virtual channels and evaluate the performance of dynamic communication of SMMN network using proposed routing algorithm under uniform traffic pattern .We also evaluate the performance of dynamic communication of TESH network using topaz simulator. It is shown that the SMMN network has high throughput and low latency, which yield higher performance of dynamic communication compare to other Hierarchical networks.
Advances in Intelligent Systems and Computing, 2014
The series "Advances in Intelligent Systems and Computing" contains publications on theory, appli... more The series "Advances in Intelligent Systems and Computing" contains publications on theory, applications, and design methods of Intelligent Systems and Intelligent Computing. Virtually all disciplines such as engineering, natural sciences, computer and information science, ICT, economics, business, e-commerce, environment, healthcare, life science are covered. The list of topics spans all the areas of modern intelligent systems and computing. The publications within "Advances in Intelligent Systems and Computing" are primarily textbooks and proceedings of important conferences, symposia and congresses. They cover significant recent developments in the field, both of a foundational and applicable character. An important characteristic feature of the series is the short publication time and worldwide distribution. This permits a rapid and broad dissemination of research results.
Lecture Notes in Computer Science, 2012
A Hierarchical 3D-Mesh (H3DM) Network is a 2D-mesh network of multiple basic modules (BMs), in wh... more A Hierarchical 3D-Mesh (H3DM) Network is a 2D-mesh network of multiple basic modules (BMs), in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher-level networks. In this paper, we evaluate the dynamic communication performance of a Hierarchical 3D-Mesh (H3DM) network using a deadlock-free routing algorithm with minimum number of virtual channels under the uniform and non-uniform traffic patterns; and compare it with other networks to show the superiority of the H3DM network over other networks. We have also evaluated the dynamic communication performance of the mesh and torus networks. It is shown that H3DM network yields low average transfer time than that of mesh and torus networks. The trade-off between throughput and latency of these networks shown that H3DM network provide better dynamic communication performance than that of mesh and torus networks before saturation.
2009 12th International Conference on Computers and Information Technology, 2009
A Symmetric Tori connected Torus Network (STTN) is a 2D-torus network of multiple basic modules, ... more A Symmetric Tori connected Torus Network (STTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 2D-torus networks that are hierarchically interconnected for higher-level networks. In this paper, we present the architecture of the STTN, addressing of node, routing of message, and evaluate the static network performance of STTN, TTN, TESH, mesh, and torus networks. It is shown that the STTN possesses several attractive features, including constant degree, small diameter, low cost, small average distance, moderate bisection width, and high fault tolerant performance than that of other conventional and hierarchical interconnection networks.
Lecture Notes in Computer Science, 2014
Midimew connected Mesh Network (MMN) is a Minimal DIstance MEsh with Wrap-around links (midimew) ... more Midimew connected Mesh Network (MMN) is a Minimal DIstance MEsh with Wrap-around links (midimew) network. In this paper, we present the architecture of MMN and evaluate the total wire length of MMN, TESH, mesh, and torus networks. It is shown that the proposed MMN possesses simple structure and moderate wire length. The total wire length of MMN is slightly higher than that of mesh network and lower than that of 2-D torus network. Overall performance suggests that, MMN is an optimal network among these networks.
Journal of Parallel and Distributed Computing, 2005
A hierarchical torus network (HTN) is a 2D-torus network of multiple basic modules, in which the ... more A hierarchical torus network (HTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher-level networks. The static network performance of the HTN and its dynamic communication performance using the popular dimension-order routing algorithm have already been evaluated and shown to be superior to the performance of other conventional and hierarchical interconnection networks. In this paper, we propose a link-selection algorithm for efficient use of physical links of the HTN, while keeping the link-selection algorithm as simple as the dimension-order routing algorithm. We also prove that the proposed algorithm for the HTN is deadlock-free using three virtual channels. We evaluate the dynamic communication performance of an HTN using dimension-order routing and link-selection algorithms under various traffic patterns. We find that the dynamic communication performance of an HTN using the link-selection algorithm is better than when the dimension-order routing algorithm is used.
Journal of Networks, 2012
A Hierarchical Torus Network (HTN) is a 2Dtorus network of multiple basic modules, in which the b... more A Hierarchical Torus Network (HTN) is a 2Dtorus network of multiple basic modules, in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher-level networks. The static network performance of the HTN and its dynamic communication performance using the deterministic, dimension-order routing algorithm have already been evaluated and shown to be superior to the performance of other conventional and hierarchical interconnection networks. However, the assessment of the dynamic communication performance improvement of HTN by the efficient use of both the physical link and virtual channels has not yet been evaluated. This paper addresses three adaptive routing algorithms-link-selection, channelselection, and a combination of link-selection and channelselection-for the efficient use of physical links and virtual channels of an HTN to enhance dynamic communication performance. It also proves that the proposed adaptive routing algorithms are deadlock-free with 3 virtual channels. The dynamic communication performances of an HTN is evaluated by using dimension-order routing and proposed adaptive routing algorithms under various traffic patterns. It is found that the dynamic communication performance of an HTN using these adaptive routing algorithms are better than when the dimension-order routing is used, in terms of network throughput.
IEICE Transactions on Information and Systems, 2005
Three-dimensional (3D) wafer stacked implementation (WSI) has been proposed as a promising techno... more Three-dimensional (3D) wafer stacked implementation (WSI) has been proposed as a promising technology for massively parallel computers. A hierarchical 3D-torus (H3DT) network, which is a 3D-torus network of multiple basic modules in which the basic modules are 3D-mesh networks, has been proposed for efficient 3D-WSI. However, the restricted use of physical links between basic modules in the higher level networks reduces the dynamic communication performance of this network. A torus network has better dynamic communication performance than a mesh network. Therefore, we have modified the H3DT network by replacing the 3D-mesh modules by 3D-tori, calling it a Modified H3DT (MH3DT) network. This paper addresses the architectural details of the MH3DT network and explores aspects such as degree, diameter, cost, average distance, arc connectivity, bisection width, and wiring complexity. We also present a deadlock-free routing algorithm for the MH3DT network using two virtual channels and evaluate the network's dynamic communication performance under the uniform traffic pattern, using the proposed routing algorithm. It is shown that the MH3DT network possesses several attractive features including small diameter, small cost, small average distance, better bisection width, and better dynamic communication performance.
IEICE Transactions on Information and Systems, 2011
A Modified Hierarchical 3D-Torus (MH3DT) network is a 3D-torus network consisting of multiple bas... more A Modified Hierarchical 3D-Torus (MH3DT) network is a 3D-torus network consisting of multiple basic modules, in which each basic module itself is a 3D-torus network. Inter-node communication performance has been evaluated using dimension-order routing and 2 virtual channels (VCs) under uniform traffic patterns but not under non-uniform traffic patterns. In this paper, we evaluate the inter-node communication performance of MH3DT under five non-uniform traffic patterns and compare it with other networks. We found that under non-uniform traffic patterns, the MH3DT yields high throughput and low latency, providing better inter-node communication performance compared to H3DT, TESH, mesh, and torus networks. Also, we found that non-uniform traffic patterns have higher throughput than uniform traffic in the MH3DT network.
Communications and Network, 2013
The Tori-connected mESH (TESH) Network is a k-ary n-cube networks of multiple basic modules, in w... more The Tori-connected mESH (TESH) Network is a k-ary n-cube networks of multiple basic modules, in which the basic modules are 2D-mesh networks that are hierarchically interconnected for higher level k-ary n-cube networks. Many adaptive routing algorithms for k-ary n-cube networks have already been proposed. Thus, those algorithms can also be applied to TESH network. We have proposed three adaptive routing algorithms-channel-selection, link-selection, and dynamic dimension reversal-for the efficient use of network resources of a TESH network to improve dynamic communication performance. In this paper, we implement these routers using VHDL and evaluate the hardware cost and delay for the proposed routing algorithms and compare it with the dimension order routing. The delay and hardware cost of the proposed adaptive routing algorithms are almost equal to that and slightly higher than that of dimension order routing, respectively. Also we evaluate the communication performance with hardware implementation. It is found that the communication performance of a TESH network using these adaptive algorithms is better than when the dimension-order routing algorithm is used.
Journal of Networks, 2009
IEICE Transactions on Information and Systems, 2009
Interconnection networks play a crucial role in the performance of massively parallel computers. ... more Interconnection networks play a crucial role in the performance of massively parallel computers. Hierarchical interconnection networks provide high performance at low cost by exploring the locality that exists in the communication patterns of massively parallel computers. A Tori connected Torus Network (TTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 2D-torus networks that are hierarchically interconnected for higher-level networks. This paper addresses the architectural details of the TTN and explores aspects such as node degree, network diameter, cost, average distance, arc connectivity, bisection width, and wiring complexity. We also present a deadlock-free routing algorithm for the TTN using four virtual channels and evaluate the network's dynamic communication performance using the proposed routing algorithm under uniform and various non-uniform traffic patterns. We evaluate the dynamic communication performance of TTN, TESH, MH3DT, mesh, and torus networks by computer simulation. It is shown that the TTN possesses several attractive features, including constant node degree, small diameter, low cost, small average distance, moderate (neither too low, nor too high) bisection width, and high throughput and very low zero load latency, which provide better dynamic communication performance than that of other conventional and hierarchical networks.
Interconnection networks play a crucial role in the per-formance of massively parallel computers.... more Interconnection networks play a crucial role in the per-formance of massively parallel computers. Hierarchical in-terconnection networks provide high performance at low cost by exploring the locality that exists in the communi-cation patterns of massively parallel computers. A ...
Applied Sciences, 2020
In order to fulfill the increasing demand for computation power to process a boundless data concu... more In order to fulfill the increasing demand for computation power to process a boundless data concurrently within a very short time or real-time in many areas such as IoT, AI, machine learning, smart grid, and big data analytics, we need exa-scale or zetta-scale computation in the near future. Thus, to have this level of computation, we need a massively parallel computer (MPC) system that shall consist of millions of nodes; and, for the interconnection of these massive numbers of nodes, conventional topologies are infeasible. Thus, a hierarchical interconnection network (HIN) is a rational way to connect huge nodes. Through this article, we are proposing a new HIN, which is a tori-connected flattened butterfly network (TFBN) for the next generation MPC system. Numerous basic modules are hierarchically interconnected as a toroidal connection, whereby the basic modules are flattened butterfly networks. We have studied the network architecture, static network performance, and static cost...
The most critical component in determining the ultimate performance potential of a multicomputer ... more The most critical component in determining the ultimate performance potential of a multicomputer is its interconnection network. In this dissertation, we propose a new hierarchical interconnection network, called the Hierarchical Torus Network (HTN) for large scale 3D multicomputers. It consists of multiple basic modules (BMs) which are 3D-tori (m × m × m) and are hierarchically interconnected by 2D-tori (n × n). Both the BMs and the interconnection at higher levels are toroidally connected, hence the name Hierarchical Torus Network (HTN). To reduce the vertical links between silicon planes, we consider higher-level networks as 2D-torus instead of 3D-torus network. We have explored various aspects such as network diameter, cost, average distance, bisection width, peak number of vertical links, and VLSI
Proceedings of the Canadian Engineering Education Association (CEEA), 2020
This paper addresses the construction of a novel approach to enhance learner motivation as it rel... more This paper addresses the construction of a novel approach to enhance learner motivation as it relates to the learning process. The foundational principles of motivation are discussed. The impact of instructional technology on student motivation through an innovative web-based problem-solving system is the main focus of this study. The development of the web-based problem-solving system and its evaluation process are considered for addressing the foundational principles of motivation. The proposed system is customizable to provide feedback to both students and instructors. The outcome of this research will help establish a suitable instructional design model of motivation for engineering students. The process also has prospects for applications in other disciplines.
Procedia Computer Science, 2015
A Symmetric Midimew Mesh connected network (SMMN) is a hierarchical interconnection networks (HIN... more A Symmetric Midimew Mesh connected network (SMMN) is a hierarchical interconnection networks (HIN) that capable to interconnect vast number of nodes that could reach up to millions of nodes in the network. SMMN has multiple basic modules of 2D-mesh networks that are recursively interconnected by Midimew network to create higher-level networks. In this paper, we explain the architectural details of SMMN ,we also present the a deadlock-free routing algorithm for SMMN using four virtual channels and evaluate the performance of dynamic communication of SMMN network using proposed routing algorithm under uniform traffic pattern .We also evaluate the performance of dynamic communication of TESH network using topaz simulator. It is shown that the SMMN network has high throughput and low latency, which yield higher performance of dynamic communication compare to other Hierarchical networks.
Advances in Intelligent Systems and Computing, 2014
The series "Advances in Intelligent Systems and Computing" contains publications on theory, appli... more The series "Advances in Intelligent Systems and Computing" contains publications on theory, applications, and design methods of Intelligent Systems and Intelligent Computing. Virtually all disciplines such as engineering, natural sciences, computer and information science, ICT, economics, business, e-commerce, environment, healthcare, life science are covered. The list of topics spans all the areas of modern intelligent systems and computing. The publications within "Advances in Intelligent Systems and Computing" are primarily textbooks and proceedings of important conferences, symposia and congresses. They cover significant recent developments in the field, both of a foundational and applicable character. An important characteristic feature of the series is the short publication time and worldwide distribution. This permits a rapid and broad dissemination of research results.
Lecture Notes in Computer Science, 2012
A Hierarchical 3D-Mesh (H3DM) Network is a 2D-mesh network of multiple basic modules (BMs), in wh... more A Hierarchical 3D-Mesh (H3DM) Network is a 2D-mesh network of multiple basic modules (BMs), in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher-level networks. In this paper, we evaluate the dynamic communication performance of a Hierarchical 3D-Mesh (H3DM) network using a deadlock-free routing algorithm with minimum number of virtual channels under the uniform and non-uniform traffic patterns; and compare it with other networks to show the superiority of the H3DM network over other networks. We have also evaluated the dynamic communication performance of the mesh and torus networks. It is shown that H3DM network yields low average transfer time than that of mesh and torus networks. The trade-off between throughput and latency of these networks shown that H3DM network provide better dynamic communication performance than that of mesh and torus networks before saturation.
2009 12th International Conference on Computers and Information Technology, 2009
A Symmetric Tori connected Torus Network (STTN) is a 2D-torus network of multiple basic modules, ... more A Symmetric Tori connected Torus Network (STTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 2D-torus networks that are hierarchically interconnected for higher-level networks. In this paper, we present the architecture of the STTN, addressing of node, routing of message, and evaluate the static network performance of STTN, TTN, TESH, mesh, and torus networks. It is shown that the STTN possesses several attractive features, including constant degree, small diameter, low cost, small average distance, moderate bisection width, and high fault tolerant performance than that of other conventional and hierarchical interconnection networks.
Lecture Notes in Computer Science, 2014
Midimew connected Mesh Network (MMN) is a Minimal DIstance MEsh with Wrap-around links (midimew) ... more Midimew connected Mesh Network (MMN) is a Minimal DIstance MEsh with Wrap-around links (midimew) network. In this paper, we present the architecture of MMN and evaluate the total wire length of MMN, TESH, mesh, and torus networks. It is shown that the proposed MMN possesses simple structure and moderate wire length. The total wire length of MMN is slightly higher than that of mesh network and lower than that of 2-D torus network. Overall performance suggests that, MMN is an optimal network among these networks.
Journal of Parallel and Distributed Computing, 2005
A hierarchical torus network (HTN) is a 2D-torus network of multiple basic modules, in which the ... more A hierarchical torus network (HTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher-level networks. The static network performance of the HTN and its dynamic communication performance using the popular dimension-order routing algorithm have already been evaluated and shown to be superior to the performance of other conventional and hierarchical interconnection networks. In this paper, we propose a link-selection algorithm for efficient use of physical links of the HTN, while keeping the link-selection algorithm as simple as the dimension-order routing algorithm. We also prove that the proposed algorithm for the HTN is deadlock-free using three virtual channels. We evaluate the dynamic communication performance of an HTN using dimension-order routing and link-selection algorithms under various traffic patterns. We find that the dynamic communication performance of an HTN using the link-selection algorithm is better than when the dimension-order routing algorithm is used.
Journal of Networks, 2012
A Hierarchical Torus Network (HTN) is a 2Dtorus network of multiple basic modules, in which the b... more A Hierarchical Torus Network (HTN) is a 2Dtorus network of multiple basic modules, in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher-level networks. The static network performance of the HTN and its dynamic communication performance using the deterministic, dimension-order routing algorithm have already been evaluated and shown to be superior to the performance of other conventional and hierarchical interconnection networks. However, the assessment of the dynamic communication performance improvement of HTN by the efficient use of both the physical link and virtual channels has not yet been evaluated. This paper addresses three adaptive routing algorithms-link-selection, channelselection, and a combination of link-selection and channelselection-for the efficient use of physical links and virtual channels of an HTN to enhance dynamic communication performance. It also proves that the proposed adaptive routing algorithms are deadlock-free with 3 virtual channels. The dynamic communication performances of an HTN is evaluated by using dimension-order routing and proposed adaptive routing algorithms under various traffic patterns. It is found that the dynamic communication performance of an HTN using these adaptive routing algorithms are better than when the dimension-order routing is used, in terms of network throughput.
IEICE Transactions on Information and Systems, 2005
Three-dimensional (3D) wafer stacked implementation (WSI) has been proposed as a promising techno... more Three-dimensional (3D) wafer stacked implementation (WSI) has been proposed as a promising technology for massively parallel computers. A hierarchical 3D-torus (H3DT) network, which is a 3D-torus network of multiple basic modules in which the basic modules are 3D-mesh networks, has been proposed for efficient 3D-WSI. However, the restricted use of physical links between basic modules in the higher level networks reduces the dynamic communication performance of this network. A torus network has better dynamic communication performance than a mesh network. Therefore, we have modified the H3DT network by replacing the 3D-mesh modules by 3D-tori, calling it a Modified H3DT (MH3DT) network. This paper addresses the architectural details of the MH3DT network and explores aspects such as degree, diameter, cost, average distance, arc connectivity, bisection width, and wiring complexity. We also present a deadlock-free routing algorithm for the MH3DT network using two virtual channels and evaluate the network's dynamic communication performance under the uniform traffic pattern, using the proposed routing algorithm. It is shown that the MH3DT network possesses several attractive features including small diameter, small cost, small average distance, better bisection width, and better dynamic communication performance.
IEICE Transactions on Information and Systems, 2011
A Modified Hierarchical 3D-Torus (MH3DT) network is a 3D-torus network consisting of multiple bas... more A Modified Hierarchical 3D-Torus (MH3DT) network is a 3D-torus network consisting of multiple basic modules, in which each basic module itself is a 3D-torus network. Inter-node communication performance has been evaluated using dimension-order routing and 2 virtual channels (VCs) under uniform traffic patterns but not under non-uniform traffic patterns. In this paper, we evaluate the inter-node communication performance of MH3DT under five non-uniform traffic patterns and compare it with other networks. We found that under non-uniform traffic patterns, the MH3DT yields high throughput and low latency, providing better inter-node communication performance compared to H3DT, TESH, mesh, and torus networks. Also, we found that non-uniform traffic patterns have higher throughput than uniform traffic in the MH3DT network.
Communications and Network, 2013
The Tori-connected mESH (TESH) Network is a k-ary n-cube networks of multiple basic modules, in w... more The Tori-connected mESH (TESH) Network is a k-ary n-cube networks of multiple basic modules, in which the basic modules are 2D-mesh networks that are hierarchically interconnected for higher level k-ary n-cube networks. Many adaptive routing algorithms for k-ary n-cube networks have already been proposed. Thus, those algorithms can also be applied to TESH network. We have proposed three adaptive routing algorithms-channel-selection, link-selection, and dynamic dimension reversal-for the efficient use of network resources of a TESH network to improve dynamic communication performance. In this paper, we implement these routers using VHDL and evaluate the hardware cost and delay for the proposed routing algorithms and compare it with the dimension order routing. The delay and hardware cost of the proposed adaptive routing algorithms are almost equal to that and slightly higher than that of dimension order routing, respectively. Also we evaluate the communication performance with hardware implementation. It is found that the communication performance of a TESH network using these adaptive algorithms is better than when the dimension-order routing algorithm is used.
Journal of Networks, 2009
IEICE Transactions on Information and Systems, 2009
Interconnection networks play a crucial role in the performance of massively parallel computers. ... more Interconnection networks play a crucial role in the performance of massively parallel computers. Hierarchical interconnection networks provide high performance at low cost by exploring the locality that exists in the communication patterns of massively parallel computers. A Tori connected Torus Network (TTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 2D-torus networks that are hierarchically interconnected for higher-level networks. This paper addresses the architectural details of the TTN and explores aspects such as node degree, network diameter, cost, average distance, arc connectivity, bisection width, and wiring complexity. We also present a deadlock-free routing algorithm for the TTN using four virtual channels and evaluate the network's dynamic communication performance using the proposed routing algorithm under uniform and various non-uniform traffic patterns. We evaluate the dynamic communication performance of TTN, TESH, MH3DT, mesh, and torus networks by computer simulation. It is shown that the TTN possesses several attractive features, including constant node degree, small diameter, low cost, small average distance, moderate (neither too low, nor too high) bisection width, and high throughput and very low zero load latency, which provide better dynamic communication performance than that of other conventional and hierarchical networks.
Interconnection networks play a crucial role in the per-formance of massively parallel computers.... more Interconnection networks play a crucial role in the per-formance of massively parallel computers. Hierarchical in-terconnection networks provide high performance at low cost by exploring the locality that exists in the communi-cation patterns of massively parallel computers. A ...