Mapping parallel algorithms into hypercubes
The hypercube network has exhibited a strong propensity for the implementation of algorithms designed for other topological structures by means of graphical embedding. Previous work in this area has been based upon two basic premises. First, a reliance upon subcube assignment as a task allocation technique has served to emphasize expansion as an important gauge of the efficiency of an embedding. Second, the store-and-forward technology of the first generation of hypercubes necessitated the development of adjacency-preserving or, at least, minimal dilation embeddings. In this thesis, the author examines recent research which drastically reduces the significance of expansion and dilation as embedding efficiency gauges. He introduces the concept of multiple graph embeddings into a single hypercube without relegating separate tasks to distinct subcubes. Successful results with quadtree and pyramid source graphs using this approach indicate that achieving optimal expansion for individual tasks is not always advantageous. Furthermore, the recent development of the direct-connect hypercube technology has effectively eliminated dilation as a serious problem with embeddings into the hypercube. He presents several algorithms for embedding specific classes of graphs into the hypercube. Unlike previous work with binary trees and rectangular meshes, these classes of graphs do not lend themselves to straightforward hypercube embeddings with low dilation and expansion values. He also examines a number of heuristic approaches for the intractable problem of embedding general graphs and trees into the hypercube. Mathematical analysis of our algorithms and statistical analysis of the heuristic methods led us to the conclusion that congestion has now become the most significant gauge by which an embedding's efficiency is measured.
- Research Organization:
- Ohio State Univ., Columbus, OH (USA)
- OSTI ID:
- 6054589
- Resource Relation:
- Other Information: Thesis (Ph.D)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
HYPERCUBE COMPUTERS
ALGORITHMS
PARALLEL PROCESSING
COMPUTER NETWORKS
GRAPHS
MESH GENERATION
TASK SCHEDULING
TOPOLOGICAL MAPPING
COMPUTERS
DATA PROCESSING
MAPPING
MATHEMATICAL LOGIC
PROCESSING
PROGRAMMING
TRANSFORMATIONS
990200* - Mathematics & Computers