Topological Properties of Hierarchical Interconnection Networks: A Review and Comparison

Abstract

Hierarchical interconnection networks (HINs) provide a framework for designing networks with reduced link cost by taking advantage of the locality of communication that exists in parallel applications. HINs employ multiple levels. Lower-level networks provide local communication while higher-level networks facilitate remote communication. HINs provide fault tolerance in the presence of some faulty nodes and/or links. Existing HINs can be broadly classified into two classes. those that use nodes and/or links replication and those that use standby interface nodes. The first class includes Hierarchical Cubic Networks, Hierarchical Completely Connected Networks, and Triple-based Hierarchical Interconnection Networks. The second HINs class includes Modular Fault-Tolerant Hypercube Networks and Hierarchical Fault-Tolerant Interconnection Network. This paper presents a review and comparison of the topological properties of both classes of HINs. The topological properties considered are network degree, diameter, cost and packing density. The outcome of this study show among all HINs two networks that is, the Root-Folded Heawood (RFH) and the Flooded Heawood (FloH), belonging to the first HIN class provide the best network cost, defined as the product of network diameter and degree. The study also shows that HFCube(n,n)provide the best packing density, that is, the smallest chip area required for VLSI implementation.

A new hypercube variant: Fractal Cubic Network Graph

“…These are the Folded Hypercube ( [2,8]), the Crossed Cube (Twisted Cube) ( [11,14,22]) and the Hierarchical Cubic Network (cf. the survey [1] and [10,17,18]) which are the most popular hypercube variants. Aims of these approaches are just to reduce the diameter of the hypercube but reserve its advantages.…”

“…If the faulted edges are not in the set E 1 (k) ¼ 11jjE 1 (kÀ1)∪01jjE1 (kÀ1) f011100; 011101; 011111; 011110; 010110; 010111; 010101; 010100g∪ f010000; 010001; 010011; 010010; 011010; 011011; 011001; 011000g∪ f001000; 001001; 001011; 001010; 000010; 000011; 000001; 000000g∪ f000100; 000101; 000111; 000110; 001110; 001111; 001101; 001100g∪ f101100; 101101; 101111; 101110; 100110; 100111; 100101; 100100g∪ f100000; 100001; 100011; 100010; 101010; 101011; 101001; 101000g∪ f111000; 111001; 111011; 111010; 110010; 110011; 110001; 110000g∪ f110100; 110101; 110111; 110110; 111110; 111111; 111101; 111100g: ∪10jjE 1 (kÀ1)∪00jjE 1 (kÀ1)∪{The FCNG 1 ðkÞ and FCNG 2 ðkÞ are variants of hypercubes. The constructions of FCNG 1 ðkÞ and FCNG 2 ðkÞ are similar to the construction of hypercubes.…”

On Uniform Traffic Pattern of Symmetric Midimew Connected Mesh Network

“…It is found a variety of HIN-based hypercube in the literature, however, it is difficult to implement due to the huge number of physical links. To resolve this problem, HIN designs with K-ary and n-cube were proposed 6,8 . However, the performance of proposed networks has no explicit relation for an interconnection network of MPC.…”

Hot-Spot Traffic Pattern on Hierarchical 3D Mesh Network

“…Many recent experimental and commercial parallel computers use direct networks for low latency and high bandwidth of inter-node communication. The hierarchical interconnection network (HIN) provides an alternative way in which several network topology can be integrated [5]. For future MPC with millions of nodes, the large diameter of conventional topologies is intolerable.…”

“…For future MPC with millions of nodes, the large diameter of conventional topologies is intolerable. Hence, HIN is an efficient way to interconnect the future MPC [5]. A variety of hypercube based HINs found in the literature, however, its huge number of physical links make it difficult to implement.…”