Abstract
Given an n-vertex simple polygon P, the problem of computing the shortest weakly visible subedge of P is that of finding a shortest line segment s on the boundary of P such that P is weakly visible from s (if s exists). In this paper, we present new geometric observations that are useful for solving this problem. Based on these geometric observations, we obtain optimal sequential and parallel algorithms for solving this problem. Our sequential algorithm runs in O(n) time, and our parallel algorithm runs in O(log n) time using O(n/log n) processors in the CREW PRAM computational model. Using the previously best known sequential algorithms to solve this problem would take O(n 2) time. We also give geometric observations that lead to extremely simple and optimal algorithms for solving, both sequentially and in parallel, the case of this problem where the polygons are rectilinear.
This research was partially done when the author was with the Department of Computer Sciences, Purdue University, West Lafayette, Indiana, and was supported in part by the Office of Naval Research under Grants N00014-84-K-0502 and N00014-86-K-0689, the National Science Foundation under Grant DCR-8451393, and the National Library of Medicine under Grant R01-LM05118.
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© 1993 Springer-Verlag Berlin Heidelberg
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Chen, D.Z. (1993). Optimally computing the shortest weakly visible subedge of a simple polygon preliminary version. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_263
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DOI: https://doi.org/10.1007/3-540-57568-5_263
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