1 research outputs found
Exploiting parallelism in n-D convex hull algorithms
PhD ThesisThe convex hull is a problem of primary importance because of its applications in
computational geometry. A number of sequential and parallel algorithms for computing
the convex hull of a finite set of points in the lower dimensions are known. In compar-
ison, the general n-D problem is not as well understood and parallel algorithms are not
so prevalent because the 2-D and 3-D methods are not easily extended to the general
case. This thesis presents parallel algorithms for evaluating the general n- D convex hull
problem (where 2-D and 3-D are special cases) using Swart's sequential algorithm. One of
our methods combines a gift-wrapping technique with partitioning and merge algorithms
> where the original list is split into p 1 partitions followed by the computation of
the subhulls using the sequential n-D gift-wrapping method. The partial hulls are then
combined using a fanin tree. The second method computes the convex hull in parallel
by wrapping around the edges until a complete facial lattice structure of the polytope is
generated.
Several parameterised versions of the proposed algorithms have been implemented on
the shared memory and message passing architectures. In the former, performance on an
Encore Multimax using Encore Parallel Threads and the more lightweight Microthread
programming utilities are examined. In the latter, performance on a transputer based
machine using CS- Tools is discussed. We have shown that our techniques will be useful
in the construction of faster algorithms which employ the n-D convex hull algorithms as
a sub-algorithmCommonwealth Scholarship
Commission in the United Kingdo