Volume 762 of the series Lecture Notes in Computer Science pp 323332
Optimally computing the shortest weakly visible subedge of a simple polygon preliminary version
 Danny Z. ChenAffiliated withDepartment of Computer Science and Engineering, University of Notre Dame
Abstract
Given an nvertex 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.
 Title
 Optimally computing the shortest weakly visible subedge of a simple polygon preliminary version
 Book Title
 Algorithms and Computation
 Book Subtitle
 4th International Symposium, ISAAC '93 Hong Kong, December 15–17, 1993 Proceedings
 Pages
 pp 323332
 Copyright
 1993
 DOI
 10.1007/3540575685_263
 Print ISBN
 9783540575689
 Online ISBN
 9783540482338
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 762
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Danny Z. Chen ^{(1)}
 Author Affiliations

 1. Department of Computer Science and Engineering, University of Notre Dame, 46556, Notre Dame, IN, USA
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