Finding Shortest Non-Crossing Rectilinear Paths in Plane Regions

A b s t r a c t . Let A be a plane region which is bounded by an outer rectangle and an inner one and has r rectangular obstacles inside the region. Let k terminal pairs lie on the outer and inner rectangular boundaries. This paper presents an efficient algorithm which finds k "non-crossing" rectilinear paths in the plane region A, each connecting a terminal pair without passing through any obstacles, whose total length is minimum. Non-crosslng paths may share common points or llne segments but do not cross each other in the plane. The algorithm runs in time O(nlogn) where n = r + k.