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arXiv · 2407.18758

On Approximating the Weighted Region Problem in Square Tessellations

Naonori Kakimura·Rio Katsu
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Abstract

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 $(\sqrt{2}+1)$-approximation. This improves the previous result of $2\sqrt{2}$.

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BibTeXRIS

Naonori Kakimura, Rio Katsu. 2024-07-26. On Approximating the Weighted Region Problem in Square Tessellations. https://arxiv.org/abs/2407.18758

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