Volume I: Parallel architectures on PARLE: Parallel Architectures and Languages Europe
Warp: an integrated solution of high-speed parallel computing
Proceedings of the 1988 ACM/IEEE conference on Supercomputing
The twisted cube topology for multiprocessors: a study in network asymmetry
Journal of Parallel and Distributed Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Embedding meshes on the star graph
Journal of Parallel and Distributed Computing
Parallel computation: models and methods
Parallel computation: models and methods
iWarp: anatomy of a parallel computing system
iWarp: anatomy of a parallel computing system
Introduction to Parallel Processing: Algorithms and Architectures
Introduction to Parallel Processing: Algorithms and Architectures
Embedding Graphs onto the Supercube
IEEE Transactions on Computers
Performance analysis of the Alpha 21364-based HP GS1280 multiprocessor
Proceedings of the 30th annual international symposium on Computer architecture
Linear array and ring embeddings in conditional faulty hypercubes
Theoretical Computer Science
A Technology-Aware and Energy-Oriented Topology Exploration for On-Chip Networks
Proceedings of the conference on Design, Automation and Test in Europe - Volume 2
Graph Theory With Applications
Graph Theory With Applications
Mapping Cycles and Trees on Wrap-Around Butterfly Graphs
SIAM Journal on Computing
Efficient Techniques for Clustering and Scheduling onto Embedded Multiprocessors
IEEE Transactions on Parallel and Distributed Systems
Computer Architecture
Optimal fault-tolerant embedding of paths in twisted cubes
Journal of Parallel and Distributed Computing
Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements
Theoretical Computer Science
Optimal Embeddings of Paths with Various Lengths in Twisted Cubes
IEEE Transactions on Parallel and Distributed Systems
Edge-pancyclicity and path-embeddability of bijective connection graphs
Information Sciences: an International Journal
Embedding a family of disjoint 3D meshes into a crossed cube
Information Sciences: an International Journal
Embedding of meshes in Möbius cubes
Theoretical Computer Science
Embedding a family of meshes into twisted cubes
Information Processing Letters
Embedding a family of disjoint multi-dimensional meshes into a crossed cube
Information Processing Letters
Constructing edge-disjoint spanning trees in locally twisted cubes
Theoretical Computer Science
An Enhanced Fault-Tolerant Routing Algorithm for Mesh Network-on-Chip
ICESS '09 Proceedings of the 2009 International Conference on Embedded Software and Systems
Edge-fault-tolerant node-pancyclicity of twisted cubes
Information Processing Letters
Topological properties of twisted cube
Information Sciences: an International Journal
Enhancing productivity in high performance computing through systematic conditioning
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Embedding multi-dimensional meshes into twisted cubes
Computers and Electrical Engineering
Pancyclicity of Restricted Hypercube-Like Networks under the Conditional Fault Model
SIAM Journal on Discrete Mathematics
Embedding hypercubes into cylinders, snakes and caterpillars for minimizing wirelength
Discrete Applied Mathematics
Independent spanning trees on twisted cubes
Journal of Parallel and Distributed Computing
Embedding of hypercubes into necklace, windmill and snake graphs
Information Processing Letters
Embeddings of circulant networks
Journal of Combinatorial Optimization
Hi-index | 5.23 |
The hypercube is one of the most popular interconnection networks since it has a simple structure and is easy to implement. An n-dimensional twisted cube, TQ"n, is an important variation of hypercube Q"n and preserves many of its desirable properties. The problem of how to embed a family of disjoint meshes (or tori) into a host graph has attracted great attention in recent years. However, there is no systematic method proposed to generate the desired meshes and tori in TQ"n. In this paper, we develop two systematic linear time algorithms for embedding disjoint multi-dimensional tori into TQ"n, n=7, as follows: (1) for a positive integer m with @?n2@?@?m@?n-4, a family of 2^m disjoint k-dimensional tori of size 2^s^"^1x2^s^"^2x...x2^s^"^k each can be embedded with unit dilation, where k=2 and @?"i"="1^ks"i@?n-m, and (2) for a positive integer m with 2@?m@?n-5, a family of 2^m disjoint k-dimensional tori of size 2^s^"^1x2^s^"^2x...x2^s^"^k each can be embedded with unit dilation, where k=2, s"i=2, @?"i"="1^ks"i@?n-m, and max"1"@?"i"@?"k{s"i}=n-2m. Moreover, we also provide similar embedding results for meshes and hypercubes. Our results mean that a family of torus-structured (mesh-structured, or hypercube-structured) parallel algorithms can be executed on the same twisted cube efficiently and in parallel.