Finding a rectilinear shortest path in R2 using corridor based staircase structures

Abstract

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(lgn)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(lgm)3/2) space complexity. © Springer-Verlag Borlin Heidelberg 2007.