Fault diameter of interconnection networks
Computers and Mathematics with Applications - Diagnosis and reliable design of VLSI systems
Hypernet: A communication-efficient architecture for constructing massively parallel computers
IEEE Transactions on Computers
Flip-Trees: Fault-Tolerant Graphs with Wide Containers
IEEE Transactions on Computers - Fault-Tolerant Computing
Topological Properties of Hypercubes
IEEE Transactions on Computers
A recursively scalable network VLSI implementation
Future Generation Computer Systems
Efficient dispersal of information for security, load balancing, and fault tolerance
Journal of the ACM (JACM)
The de Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI
IEEE Transactions on Computers
On the fault-diameter of the star graph
Information Processing Letters
Information Processing Letters
Topological properties of WK-recursive networks
Journal of Parallel and Distributed Computing
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
Combinatorial Analysis of the Fault-Diameter of the N-Cube
IEEE Transactions on Computers
Properties and Performance of Folded Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Algorithms and Properties of a New Two-Level Network with Folded Hypercubes as Basic Modules
IEEE Transactions on Parallel and Distributed Systems
A General Broadcasting Scheme for Recursive Networks with Complete Connection
ICPADS '98 Proceedings of the 1998 International Conference on Parallel and Distributed Systems
An oblivious shortest-path routing algorithm for fully connected cubic networks
Journal of Parallel and Distributed Computing
Node-disjoint paths in a level block of generalized hierarchical completely connected networks
Theoretical Computer Science
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The purpose of this paper is to investigate combinatorial properties of the hypernet network. The hypernet network owns two structural advantages: expansibility and equal degree. Besides, it was shown efficient in both communication and computation. Since the number of nodes contained in the hypernet network increases very rapidly with expansion level, we emphasize the hypernet network of two levels (denoted by HN$(d, 2)$) with a practical view. Recently, combinatorial properties such as container (i.e., node-disjoint paths), wide diameter, and fault diameter have received much attention due to their increasing importance and applications in networks. In this paper, the following results are obtained for HN$(d, 2)$: 1) best containers with width $d-1$, 2) containers with (maximum) width $d$, 3) the ($d-1$)-wide diameter, 4) the $d$-wide diameter, 5) the $(d - 2)$-fault diameter, and 6) the $(d-1)$-fault diameter. More specifically, between every two nodes of HN$(d, 2)$, $d$ (or $d-1$) packets can be transmitted simultaneously with at most $D + 2$ (or $D + 1$) parallel steps, where $D=2d+1$ is the diameter of HN$(d, 2)$. Besides, the diameter of HN$(d, 2)$ will increase by at most two (or one), if there are at most $d-1$ (or $d-2$) node faults. Our results reveal that HN$(d, 2)$ is not only efficient in parallel transmission, but robust in fault tolerance.