Rectilinear shortest paths through polygonal obstacles in O(n(logn)2) time
SCG '87 Proceedings of the third annual symposium on Computational geometry
Efficient algorithms for Euclidean shortest path and visibility problems with polygonal obstacles
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
An output-sensitive algorithm for computing visibility
SIAM Journal on Computing
An Optimal Algorithm for Euclidean Shortest Paths in the Plane
SIAM Journal on Computing
Efficiently Constructing the Visibility Graph of a Simple Polygon with Obstacles
SIAM Journal on Computing
Planar rectilinear shortest path computation using corridors
Computational Geometry: Theory and Applications
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The rectilinear shortest path problem can be stated as - given a set of m non-intersecting simple polygonal obstacles in the plane, find a shortest rectilinear (L1) path from a point s to a point t which avoids all the obstacles. The path can touch an obstacle but does not cross it. This paper presents an algorithm with time complexity O(n + m(lg n)3/2), which is close to the known lower bound of Ω(n + m lg m) for finding such a path. Here, n is the number of vertices of all the obstacles together. Our algorithm is of O(n +m(lg m)3/2) space complexity.