Planar point location using persistent search trees
Communications of the ACM
Art gallery theorems and algorithms
Art gallery theorems and algorithms
An efficient algorithm for link-distance problems
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Shortest watchman routes in simple polygons
Discrete & Computational Geometry
An Optimal Algorithm for Detecting Weak Visibility of a Polygon
IEEE Transactions on Computers
A simple algorithm for determining the envelope of a set of lines
Information Processing Letters
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Computational geometry column 18
ACM SIGACT News
Watchman routes under limited visibility
Computational Geometry: Theory and Applications
An O(n log n) algorithm for computing the link center of a simple polygon
Discrete & Computational Geometry
Optimal linear-time algorithm for the shortest illuminating line segment in a polygon
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Optimally computing the shortest weakly visible subedge of a simple polygon
Journal of Algorithms
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
An Optimal Algorithm for Finding the Kernel of a Polygon
Journal of the ACM (JACM)
Finding all weakly-visible chords of a polygon in linear time
Nordic Journal of Computing
Computing a Shortest Watchman Path in a Simple Polygon in Polynomial-Time
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Computing in Linear Time a Chord from Which a Simple Polygon is Weakly Internally Visible
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
Rotationally monotone polygons
Computational Geometry: Theory and Applications
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A simple polygon is said to be weakly internally visible from a line segment lying inside it if every point on the boundary of the polygon is visible from some point on the line segment. In this paper, we present an optimal linear-time algorithm for the following problem: Given a simple polygon, either compute a shortest line segment from which the polygon is weakly internally visible, or report that the polygon is not weakly internally visible.The algorithm presented is conceptually simple. This paper also incorporates a significant improvement over the linear-time algorithm for the same problem, presented in a preliminary version [12], in the sense that it eliminates the need for using two complicated preprocessing tools: Chazelle's linear-time triangulation algorithm [7], and the algorithm for computing single-source-shortest-paths from a specified vertex in a triangulated polygon [16], thus making the algorithm practical.