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• W1850028945 abstract "Constant-work-space algorithms may use only constantly many cells of storage in addition to their input, which is provided as a read-only array. We show how to construct several geometric structures eciently in the constant-work-space model. Traditional algo- rithms process the input into a suitable data structure (like a doubly-connected edge list) that allows ecient traversal of the structure at hand. In the constant-work-space setting, however, we cannot aord to do this. Instead, we provide operations that compute the desired features on the y by accessing the input with no extra space. The whole geomet- ric structure can be obtained by using these operations to enumerate all the features. Of course, we must pay for the space savings by slower running times. While the standard data structure allows us to implement traversal operations in constant time, our schemes typically take linear time to read the input data in each step. We begin with two simple problems: triangulating a planar point set and nding the trapezoidal decomposition of a simple polygon. In both cases adjacent features can be enumerated in linear time per step, resulting in total quadratic running time to output the whole structure. Actually, we show that the former result carries over to the Delaunay triangulation, and hence the Voronoi diagram. This also means that we can compute the largest empty circle of a planar point set in quadratic time and constant work-space. As another application, we demonstrate how to enumerate the features of an Euclidean minimum spanning tree (EMST) in quadratic time per step, so that the whole EMST can be found in cubic time using constant work-space." @default.
• W1850028945 created "2016-06-24" @default.
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• W1850028945 date "2010-10-08" @default.
• W1850028945 modified "2023-09-23" @default.
• W1850028945 title "CONSTANT-WORK-SPACE ALGORITHMS FOR GEOMETRIC PROBLEMS" @default.
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