Let S be a planar n-point set. A triangulation for S is a maximal plane straight-line graph with vertex set S. The Voronoi diagram for S is the subdivision of the plane into cells such that each cell has the same nearest neighbors in S. Classically, both structures can be computed in O(n log n) time and O(n) space. We study the situation when the available workspace is limited: given a parameter s S {1,...,n}, an s-workspace algorithm has read-only access to an input array with the points from S in arbitrary order, and it may use only O(s) additional words of θ(log n) bits for reading and writing intermediate data. The output should then be written to a write-only structure. We describe a deterministic s-workspace algorithm for computing a triangulation of S in time O(n~2/s + n log n log s) and a randomized s-workspace algorithm for finding the Voronoi diagram of S in expected time O((n~2/s)log s + n log s log~* s).
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机译:令S为平面n点集。 S的三角剖分是顶点集为S的最大平面直线图。S的Voronoi图是将平面细分为像元,以便每个像元在S中具有相同的最近邻居。 O(n log n)时间和O(n)空间。我们研究了可用工作空间有限的情况:给定参数s S {1,...,n},s工作空间算法对输入数组具有只读访问权限,该输入数组具有来自S的点以任意顺序排列,并且它可以仅使用θ(log n)位的O(s)个附加字来读写中间数据。然后应将输出写入只写结构。我们描述了一种确定性s-工作区算法,用于计算S在时间O(n〜2 / s + n log n log s)中的三角剖分,以及一种随机s-工作区算法,用于在预期时间O(( n〜2 / s)log s + n log s log〜* s)。
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