The weighted region problem is the problem of finding the weighted shortest path on a plane consisting of polygonal regions with different weights. For the case when the plane is tessellated by squares, we can solve the problem approximately by finding the shortest path on a grid graph defined by placing a vertex at the center of each grid. In this note, we show that the obtained path admits (2+1)-approximation. This improves the previous result of 22.
@article{arxiv.2407.18758,
title = {On Approximating the Weighted Region Problem in Square Tessellations},
author = {Naonori Kakimura and Rio Katsu},
journal= {arXiv preprint arXiv:2407.18758},
year = {2024}
}