Document Type
Thesis
Date of Award
8-30-1991
Degree Name
Master of Science in Electrical Engineering - (M.S.)
Department
Electrical and Computer Engineering
First Advisor
Sotirios Ziavras
Second Advisor
Edwin Hou
Third Advisor
John D. Carpinelli
Abstract
Hierarchically structured arrays of processors are appropriate for low-level and intermediate-level image processing and computer vision. The most widely used structure is the pyramid. Neverthless, pyramid machines do not support the efficient implementation of the majority of scientific algorithms and their cost may become prohibitively high. In contrast, hypercube machines efficiently implement a wide variety of important algorithms due to the versatility of the underlying network. In fact, hypercube-based systems have become commercially available. The hypercube network supports both regular and irregular communications and it can efficiently simulate a variety of other structures like rings, trees, meshes, pyramids, etc. Thus, algorithms have been developed for the efficient simulation of the pyramid on the hypercube. Several techniques have been proposed for mapping the pyramid onto the hypercube. Stout [6], and Lai and White [12] have proposed various algorithms that map the pyramid onto the hypercube. This thesis carries out a comparative analysis of these algorithms. Stout's algorithm is cost-effective, as it needs a 2n-dimensional hypercube to map a pyramid with 71 + 1 levels, but may simulate only a single level of the pyramid at a time. Lai and White have proposed two mapping algorithms. Lai-White's algorithms perform better than Stout's algorithm when multiple levels of the pyramid need to be active concurrently. However, Stout's algorithm outperforms them in terms of cost as Lai-White's algorithms require a (2n + 1)-dimensional hypercube for the mapping of a pyramid with n, + 1 levels. This thesis also proposes a mapping algorithm that requires the same number of processors as Stout's algorithm. However, the proposed algorithm is more powerful than Stout's algorithm bacause it allows the concurrent simulation of multiple pyramid levels. Thus, the new algorithm is a compromise between Stout's algorithm and Lai-White's algorithms with respect to cost and performance. The new algorithm performs slightly worse than Lai-White's algorithms when all levels of the pyramid need to be active simultaneously, since all levels may be active concurrently in Lai-White's algorithms, while all levels, excluding the leaf level, may be active concurrently in the new algorithm. The proposed new algorithm is also extended for the mapping of multilevel structures onto the hypercube. The mappings of overlapped multilevel structures and multiple pyramids onto the hypercube are also discussed. The comparative analysis of the above algorithms is supported with the incorporation of simulation results.
Recommended Citation
Patel, Sandip C., "Mapping hierarchical structures onto hypercubes" (1991). Theses. 2581.
https://digitalcommons.njit.edu/theses/2581
