Generalized gray codes and embedding in hypercubes
Graph embedding is a fundamental problem in parallel processing. Portability of algorithms among different machines depends on the ability to suitably map the problem onto the desired architecture. Such portability is essential if existing algorithms are to run efficiently on new architectures. The general graph-embedding problem has long been known to be NP-complete. For this reasons, one must look at highly structured graphs in order to achieve easy embeddability. One active area of research has concentrated on the binary hypercube as a target architecture. The binary hypercube is a specific instance of a more general class of architecture, called generalized, base-b hypercubes. Hypercubes are prominent for a number of reasons, including rich interconnection topology, low diameter, high communication bandwidth, good fault tolerance, and efficient routing algorithms. An important tool used for embedding certain topologies in the binary hypercube is the binary Gray code. The theory of binary Gray codes is extended to include generalized, base-b Gray codes. Also presented is a new algorithm for embedding binary trees in binary hypercubes.
- Research Organization:
- Oklahoma Univ., Norman, OK (USA)
- OSTI ID:
- 7184503
- Country of Publication:
- United States
- Language:
- English
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