An algorithm for finding a region with the minimum total l1 from prescribed terminals

Abstract

Given k terminals and n axis-parallel rectangular obstacles on the plane, our algorithm finds a plane region R* such that, for any point p in R*, the total length of the k shortest rectilinear paths connecting p and the k terminals without passing through any obstacle is minimum. The algorithm is outputsensitive, and takes 0((K + n)log n) time and 0(K + n) space if k is a fixed constant, where K is the total number of polygonal vertices of the found region R.