Comparable Hypercube Research Articles

The bicube: an interconnection of two hypercubes

We consider two definitions of the even-dimensional hypercube given in the literature. The labelled graphs obtained by two definitions are not same, but one is isomorphic to the other. By interconnecting two labelled graphs in such a way that each pair of vertices with the same label are joined by an edge, we construct a vertex-symmetric graph with the diameter about half that of a comparable hypercube. We extend the result to a general scheme for interconnecting two hypercubes to produce a network topology called the bicube. We show that the bicube preserves the vertex-symmetry, bipartiteness, hamiltonian and bipancyclic properties of the hypercube, and is highly edge-symmetric.

Node‐disjoint paths and related problems on hierarchical cubic networks

AbstractAn n‐dimensional hierarchical cubic network [denoted by HCN(n)] contains 2n n‐dimensional hypercubes. The diameter of the HCN(n), which is equal to n + ⌊(n + 1)/3⌋ + 1, is about two‐thirds the diameter of a comparable hypercube, even though it uses about half as many links per node. In this paper, a maximal number of node‐disjoint paths are constructed between every two distinct nodes of the HCN(n). Their maximal length is bounded above by n + ⌊n/3⌋ + 4, which is nearly optimal. The (n + 1)‐wide diameter and n‐fault diameter of the HCN(n) are shown to be n + ⌊n/3⌋ + 3 or n + ⌊n/3⌋ + 4, which are about two‐thirds those of a comparable hypercube. Our results reveal that the HCN(n) has a smaller wide diameter and fault diameter than those of a comparable hypercube. © 2002 Wiley Periodicals, Inc.

Comments on "Hierarchical cubic networks"

Ghose and Desai (1995) introduced a new interconnection for large-scale distributed memory multiprocessors called the Hierarchical Cubic Network (HCN). The HCN is topologically superior to a comparable hypercube. They also proposed optimal routing algorithms for the HCN and obtained its diameter, which is about three-fourths the diameter of a comparable hypercube. However, their routing algorithm is not distance-optimal. In this paper, we propose an optimal routing algorithm for the HCN and show that HCN has about two-thirds the diameter of a comparable hypercube.

Extended Fibonacci Cubes

The Fibonacci Cube is an interconnection network that possesses many desirable properties that are important in network design and application. The Fibonacci Cube can efficiently emulate many hypercube algorithms and uses fewer links than the comparable hypercube, while its size does not increase as fast as the hypercube. However, most Fibonacci Cubes (more than 2/3 of all) are not Hamiltonian. In this paper, we propose an Extended Fibonacci Cube (EFC/sub 1/) with an even number of nodes. It is defined based on the same sequence F(i)=F(i-1)+F(i-2) as the regular Fibonacci sequence; however, its initial conditions are different. We show that the Extended Fibonacci Cube includes the Fibonacci Cube as a subgraph and maintains its sparsity property. In addition, it is Hamiltonian and is better in emulating other topologies. Specifically, the Extended Fibonacci Cube can embed binary trees more efficiently than the regular Fibonacci Cube and is almost as efficient as the hypercube, even though the Extended Fibonacci Cube is a much sparser network than the hypercube. We also propose a series of Extended Fibonacci Cubes with even number of nodes. Any Extended Fibonacci Cube (EFC/sub k/, with k/spl ges/) in the series contains the node set of any other cube that precedes EFC/sub k/ in the series. We show that any Extended Fibonacci Cube maintains virtually all the desirable properties of the Fibonacci Cube. The EFC/sub k/s can be considered as flexible versions of incomplete hypercubes, which eliminates their restriction on the number of nodes, and, thus, makes it possible to construct parallel machines with arbitrary sizes.

Hierarchical Hypercube Networks (HHN) for Massively Parallel Computers

The hypercube is one of the most widely used topologies because it provides small diameter and embedding of various interconnection networks. For very large systems, however, the number of links needed with the hypercube may become prohibitively large. In this paper, we propose a hierarchical interconnection network based on hypercubes called hierarchical hypercube network (HHN) for massively parallel computers. The HHN has a smaller number of links than the comparable hypercube and in particular, when we construct networks with 2Knodes, the node degree of HHN with the minimum node degree isO([formula]) while that of hypercube isO(K). Regardless of its smaller node degree, many parallel algorithms can be executed in HHN with the same time complexity as in the hypercube.

Hierarchical cubic networks

We introduce a new interconnection network for large-scale distributed memory multiprocessors called the hierarchical cubic network (HCN). We establish that the number of routing steps needed by several data parallel applications running on a HCN-based system and a hypercube-based system are about identical. Further, hypercube connections can be emulated on the HCN in constant time. Simulation of uniform and localized traffic patterns reveal that the normalized average internode distances in a HCN are better than in a comparable hypercube. Additionally, the HCN also has about three-fourths the diameter of a comparable hypercube, although it uses about half as many links per node-a fact that has positive ramifications on the implementation of HCN-connected systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>