Visibility of disjoint polygons
Algorithmica
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Common intersections of polygons
Information Processing Letters
Planning algorithm for a convex polygonal object in two-dimensional polygonal space
Discrete & Computational Geometry
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
An introduction to parallel algorithms
An introduction to parallel algorithms
Computational Geometry: Theory and Applications
Efficient Geometric Algorithms on the EREW PRAM
IEEE Transactions on Parallel and Distributed Systems
Construction of 1-d lower envelopes and applications
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
An optimal hidden-surface algorithm and its parallelization
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
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Given a collection of segments in the plane, if we regard the segments as opaque barriers, their upper envelope consists of the portions of the segments visible from point (0,+\infty). In this paper, we present deterministic parallel methods for constructing the upper envelope of segments on the weakest shared-memory model, the EREW PRAM. We show that we can find the upper envelope of n line segments optimally in O(\log n) time using O(n) processors. Furthermore, if the segments are nonintersecting and their endpoints are sorted in x-coordinate, then we can reduce the number of processors to O(n/\log n). Our method implies that we can find the upper envelope sequentially in O(n\log \log n) time, which improves previous results. We also show that we can find the upper envelope of nk-intersecting segments (any pair of the segments intersects at most k times) with a slightly larger time and processor bound.