Abstract
The rectilinear shortest path problem can be stated as follows: given a set of m non-intersecting simple polygonal obstacles in the plane, find a shortest L 1 -metric (rectilinear) path from a point s to a point t that 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.
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