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Given a 2-D binary image of size nxn, Euclidean Distance Map (EDM) is a 2-D array of the same size such that each element is storing the Euclidean distance to the nearest black pixel. It is known that a sequential algorithm can compute the EDM in O(n2) and thus this algorithm is optimal. Also, work-time optimal parallel algorithms for shared memory model have been presented. However, these algorithms...
The paper introduced recursive algorithm of fractal graphics, put forward fractal graphics parallel algorithm. Analyzing recursive algorithmic time complexity and speedup rate of the parallel algorithm. The experimental results of PC cluster show that the theoretical analysis and the experimental results of fractal graphics parallel algorithm are consistency with a marked speedup rate.
This paper's main result is presenting a new conception in the geometric modeling and visualization - a generalized efficient parallel-and-recursive algorithm with optimal bound complexity O(log2N). Voronoi diagram is one of key elements the algorithm. The algorithm solves in unified manner the variety of interrelated geometrical problems for the construction of visual models of complex phenomena...
This paper proposes a new parallel algorithm for the maximal elements problem with no constraints. It is proposed for a linear array with reconfigurable pipelined bus system (LARPBS) model and on its latest variant, LARPBS(p) model also. It runs in O(log log n ldr log n) time with O(n) processors. Its significance is that it works for any instance of the problem with no constraint laid in [2].
Spacefilling curves (SFCs) are widely used for parallel domain decomposition in scientific computing applications. The proximity preserving properties of SFCs are expected to keep most accesses local in applications that require efficient access to spatial neighborhoods. While experimental results are used to confirm this behavior, a rigorous mathematical analysis of SFCs turns out to be rather hard...
We present the first parallel algorithm for building a Hausdorff Voronoi diagram (HVD). Our algorithm is targeted towards cluster computing architectures and computes the Hausdorff Voronoi diagram for non-crossing objects in time O((n log4 n)/p) for input size n and p processors. In addition, our parallel algorithm also implies a new sequential HVD algorithm that constructs HVDs for non-crossing objects...
We introduce a scheme for static analysis that allows us to partition large geometric datasets at multiple levels of granularity to achieve both load balancing in parallel computations and minimal access to secondary memory in out-of-core computations. The idea is illustrated and fully exploited for the case of isosurface extraction, but extendible to a class of algorithms based on a small set of...
Recently it has been noticed that for semigroup computations and for selection, rectangular meshes with multiple broadcasting yield faster algorithms than their square counterparts. The contribution of the paper is to provide yet another example of a fundamental problem for which this phenomenon occurs. Specifically, we show that the problem of computing the convex hull of a set of n sorted points...
We are given a set of n points moving continuously along given trajectories in d-dimensional Euclidean space. At each instant, these sites define a Voronoi diagram which changes continuously over time except of certain critical instances, so-called topological events. We present an algorithm for maintaining the Voronoi diagram in parallel over time using only O(1) time per event on a CREW PRAM with...
A novel approximation of Euclidean distance in Z/sup 2/ is proposed, and a novel algorithm for the computation of Voronoi tessellation and Delauney triangulation is presented based on this approximation. The proposed method has low computational complexity (of order O(1/N)) and allows parallel implementation. Mathematical morphology is used to implement the Voronoi tessellation and the Delauney triangulation...
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