Rectilinear shortest paths through polygonal obstacles in O(n(logn)2) time

摘要

The problem of finding a rectilinear shortest path amongst obstacles may be stated as follows: Given a set of obstacles in the plane find a shortest rectilinear (L1) path from a point s to a point t which avoids all obstacles. The path may touch an obstacle but may not cross an obstacle. We study the rectilinear shortest path problem for the case where the obstacles are non-intersecting simple polygons, and present an &Ogr;(n (logn)2) algorithm for finding such a path, where n is the number of vertices of the obstacles. We also study the case of rectilinear obstacles in three dimensions, and show that L1 shortest paths can be found in &Ogr;(n2(log n)3) time.