Finding a Region with the Minimum Total L 1 Distance 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 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*.

DOI: 10.1007/s00453-002-0997-y

Cite this paper

@article{Takao2002FindingAR, title={Finding a Region with the Minimum Total L 1 Distance from Prescribed Terminals}, author={Yoshiyuki Takao}, journal={Algorithmica}, year={2002}, volume={35}, pages={225-256} }