| Article ID: | iaor20117031 |
| Volume: | 35 |
| Issue: | 3 |
| Start Page Number: | 225 |
| End Page Number: | 256 |
| Publication Date: | Mar 2003 |
| Journal: | Algorithmica |
| Authors: | Nishizeki Takao, Kusakari Yoshiyuki |
| Keywords: | combinatorial optimization |
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 output‐sensitive, and takes O((K+n) log n) time and O(K+n) space if k is a fixed constant, where K is the total number of polygonal vertices of the found region R*.