Natural cycletrees, formally defined in this report, is a subclass of Hamiltonian graphs with maximum degree 3 that contain a binary spanning tree. A natural cycletree used as an interconnection network thus supports directly broadcasting through the binary tree as well as nearest-neighbour communication through the cycle. Natural cycletrees have several other interesting properties, e.g., they are planar, easily extensible and can be contracted using the same methods as for binary trees. The two main results of the paper are: (i) Given an arbitrary basic binary spanning tree, there exists a natural cycletree with a minimal number of edges. (ii) Given a set of vertices, we present an algorithm for constructing a natural cycletree such that it has a minimal number of edges, its binary spanning tree has the minimal total path length and its structure satisfies a given abstract specification. For example, if we wish to construct a natural cycletree connecting k processing elements, we could invoke the algorithm with a set of k distinct vertices and a simple specification (provided as an example in the paper).
|
866
|
Algorithmic graph theory and perfect graphs
– Golumbic
- 1980
|
|
176
|
The parallel execution of DO loops
– Lamport
- 1974
|
|
153
|
Fat-trees: Universal networks for hardwareefficient supercomputing
– Leiserson
- 1985
|
|
128
|
On the mapping problem
– Bokhari
- 1981
|
|
86
|
Highly Parallel Computing
– Almasi, Gottlieb
- 1989
|
|
74
|
On the Number of Operations Simultaneously Executable in Fortran-Like Programs and Their Resulting Speedup
– Kuck, Muraoka, et al.
- 1972
|
|
49
|
Analysis of chordal ring networks
– Arden, Lee
- 1981
|
|
49
|
The de bruijn multiprocessor network: A versatile parallel processing and sorting network for vlsi
– Samatham, Pradhan
- 1989
|
|
38
|
The Warp computer: Architecture, implementation, and performance
– Annaratone
- 1987
|
|
38
|
Communications structures for large networks of microcomputers
– Wittie
- 1981
|
|
31
|
The performance of multicomputer interconnection networks
– Reed
- 1987
|
|
30
|
Hypertree: A multiprocessor interconnection topology
– Goodman, Séquin
- 1981
|
|
27
|
Systolic priority queues
– Leiserson
- 1979
|
|
23
|
Reforming compilation of logic programs
– Millroth
- 1991
|
|
21
|
The hyper-deBruijn networks: Scalable versatile architecture
– Ganesan, Pradhan
- 1993
|
|
18
|
X-Tree: A tree structured multiprocessor computer architecture
– Despain, Patterson
- 1978
|
|
16
|
Parallel Algorithms: Design and Analysis
– Chaudhuri
- 1992
|
|
16
|
Simulating Binary Trees on Hypercubes
– Monien, Sudborough
- 1988
|
|
14
|
The binary tree as an interconnection network: Applications to multiprQcessor systems and VLSI
– Horowitz, Zorat
- 1981
|
|
13
|
Graph embeddings 1988: recent breakthroughs, new directions
– Rosenberg
- 1988
|
|
10
|
Optimal Distance Networks of Low Degree for Parallel Computers
– Beivide, Herrada, et al.
- 1991
|
|
9
|
Evaluating the Performance of Multicomputer Configurations
– Agrawal, Janakiram, et al.
- 1986
|
|
9
|
Embedding Mesh of Trees in the Hypercube
– Efe
- 1991
|
|
7
|
Multiple Network Embeddings into Hypercubes
– Gupta, Hambrusch
- 1993
|
|
7
|
Embedding of treelike graphs into 2-dimensional meshes
– Zienicke
- 1991
|
|
6
|
The Art of Computer Programming (Second Edition), volume 1
– Knuth
- 1973
|
|
6
|
Embedding the complete tree in the hypercube
– Wagner
- 1994
|
|
5
|
Efficient Embeddings of Binary Trees in VLSI Arrays
– Gordon
- 1987
|
|
5
|
Minimum edge length planar embeddings of trees
– Ruzzo, Snyder
- 1981
|
|
4
|
A dictionary machine for VLSI
– Ottman, Rosenberg, et al.
- 1982
|
|
4
|
On implementing large binary tree architectures in VLSI and WSI
– Youn, Singh
- 1989
|
|
3
|
Bounded Quantifications for Iteration and Concurrency
– Barklund
- 1994
|
|
3
|
The Sneptree | a versatile interconnection Network". In
– Li, Martin
- 1986
|
|
3
|
A distributed algorithm for embedding trees in hypercubes with modifications for run-time fault tolerance
– Provost, Melhem
- 1992
|
|
3
|
Cost-performance bounds for multimicrocomputer networks
– Reed, Schwetman
- 1983
|
|
3
|
Embedding all binary trees in the hypercube
– Wagner
- 1993
|
|
2
|
Dictionary Machine with Improved Performance
– Goyal, Narayanan
- 1988
|
|
2
|
Towards Systolizing Compilation: An Overview, in
– Lengauer
- 1989
|
|
2
|
A Random, Distributed Algorithm to Embed Trees in Partially Faulty Processor Arrays
– Sitaram, Koren, et al.
- 1991
|
|
2
|
An optimal structure that accommodates both a ring and a binary tree
– Xie, Ge
- 1991
|
|
1
|
Bounded Contractions of Full Trees
– Barak, Ben-Natan
- 1993
|
|
1
|
On the Power of One Dimensional Vectors of Processors
– Bentley, Ottmann
- 1980
|
|
1
|
Simulation of Binary Trees and XTrees
– Dingle, Sudborough
- 1993
|
|
1
|
On Performing Robust Order Statistics in Tree-Structured Dictionary
– Goodrich, Atallah
- 1990
|
|
1
|
The Physical Mapping Problem for Parallel Architectures
– Heath, Rosenberg, et al.
- 1988
|
|
1
|
On Embedding Interconnection Networks into
– Hromkovitc, Muller, et al.
- 1992
|
|
1
|
A Novel Sorting Array
– Lam
- 1992
|
|
1
|
Efficient Approach to Embed Binary Trees
– Latifi, El-Amawy
- 1990
|
|
1
|
Initial Performance of the DADO2
– Stolfo
- 1987
|
|
1
|
A Systolic Array Parallelizing
– Tseng
- 1990
|
|
