# TFBN: A Cost Effective High Performance Hierarchical Interconnection Network
## 1 Introduction
In addition, food security is quite important and challenging especially in a natural disaster and pandemic situation. It is worth noting that it is important for food importing countries like Saudi Arabia and other Gulf countries. The central management of food management ranging from crop production and reservation to distribution and flood protection will be convenient with the use of the MPC system. Gene analysis and modification can easily be done with the help of an MPC system for breeding new kinds of crops like rice, or wheat, or corn which can easily be grown in the desert with less water. The modeling and simulation of many complex and dynamic problems, generally which will be very expensive and sometimes impractical or even impossible to demonstrate physically, can easily be carried with the help of an MPC system. The fastest supercomputer right now in the world is Fugaku yielded 513 petaflops performance, whereby 158,976 nodes are interconnected by 6D torus using Tofu D interconnect [1; 13] followed by Summit and Sierra interconnected 4356 and 4320 nodes, respectively by fat-tree topology [14]. After that, Sunway Taihulight and Tianhe 2A interconnected 40,960 and 16,000 nodes, respectively, by mesh topology [15]. Here, it is to be noted that each node consists of many-core, i.e., each supercomputer or an MPC system uses millions of cores. For instance, the Fugaku uses 7,299,072 cores to construct this MPC system [13]. Thus, it is depicted that the contemporary supercomputer or an MPC system interconnects thousands of nodes using conventional topologies like higher dimensional mesh or torus or fat-tree topology. A higher-dimensional regular torus network is a widely acceptable topology right now. The heat dissipation and thus the power consumption of a higher dimensional network is high compared to that of a lower-dimensional network. This phenomenon is revealed in the Fugaku supercomputer. Here, it requires 28.34 Megawatt power, which is 2.8 times more than its counter rival Summit [13]. As mentioned earlier, a low-dimensional network is better [16; 17; 18]. However, to interconnect millions of nodes, a conventional low-dimensional network is not suitable [19; 20; 21; 22; 23]. Therefore, low dimensional hierarchical interconnection networks (HIN) topology are indispensable to interconnect more than 1 million nodes for the future generation MPC system [24; 25; 26]. Considering many design attributes of an MPC system such as better inter-node communication performance (especially in terms of low latency and high throughput), low power consumption, and quick reconfiguration and high fault tolerance. The HIN combines the good attributes of many conventional networks. Many HINs have been proposed already viz., completely connected based HIN, hypercube based HIN, tree-based HIN, \(k\)-ary \(n\)-cube-based HIN, etc. However, none of these HINs are practically implemented even though they have some merits and demerits. Therefore, further investigation and exploration of HIN are needed. In this research, we have proposed a time-cost effective and high performance and novel hierarchical interconnection network for the next generation MPC system. The proposed HIN consists of numerous basic modules, and these are connected among themselves in a hierarchical manner to form the consequent higher-level networks. The basic modules are a 2D-flattened butterfly network, whereas the higher-level network is a 2D-torus network. The higher-level networks are constructed by considering immediate lower-level networks as a network module and these modules are interconnected as a 2D-torus connection. The proposed HIN is the combination of flattened butterfly network and regular 2D-torus network, and thus it is called the Tori-connected Flattened Butterfly Network (TFBN). We have considered the 2D-torus network for higher-level networks because of its regular connection pattern, and a wrap-around link between end-to-end nodes provides an alternative path to reduce the congestion and contention and increase the throughput.