Parallel algorithms on modified SIMD machines
Parallel algorithms have been extensively studied due to advancement of VLSI technology. The machine models of concern in this thesis are in the classes of SIMD computers and systolic computers. In the first part of the thesis, the parallel algorithm design for computational geometry problems in which large amount of data routing is involved is looked at. For this issue, an architecture of a modified SIMD, under which parallel algorithms without incurring data routing time can be obtained is proposed. Within this model, there are O(log(n)2) time algorithms for the following computational geometry problems; where n is the input size. 1) Convex Hull; 2) Common Intersection of Halfplanes; and 3) Maximal Elements of a Set. In the second part of the thesis, the graph-theoretic problems under the tree-structured systolic computers (TSSC) are dealt with. Using the model of TSSC the following problems in O(n2/p) time, where n is the number of vertices in a graph G, p is the number of PE's in TSSC, for 1 less than or equal to p less than or equal to n have been solved. 1) Find the connected components of an undirected graph G. 2) Find the transitive closure of an undirected graph G. 3) Find a minimum spanning tree of a connected, undirected graph G. 4) Find bridges of a connected, undirected graph G. In the third part of the thesis, the matrix operation problems under the variations of TSSC's are studied. The traditional tree structured computers are slightly modified and have obtained 1) a matrix multiplication algorithm that runs in O(n) time by using O(n2) PE's, and 2) a matrix inversion algorithm that runs in O(nlog(n)) time by using O(n2) PE's.
- OSTI ID:
- 5900889
- Country of Publication:
- United States
- Language:
- English
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