M-Guarding in K-Visibility

📝 Original Info

• Title: M-Guarding in K-Visibility
• ArXiv ID: 2510.25567
• Date: 2025-10-29
• Authors: 정보 없음 (논문에 저자 정보가 제공되지 않았습니다.)

📝 Abstract

We explore the problem of $M$-guarding polygons with holes using $k$-visibility guards, where a set of guards is said to $M$-guard a polygon if every point in the polygon is visible to at least $M$ guards, with the constraint that there may only be 1 guard on each edge. A $k$-visibility guard can see through up to $k$ walls, with $k \geq 2$. We present a theorem establishing that any polygon with holes can be 2-guarded under $k$-visibility where $k \geq 2$, which expands existing results in 0-visibility. We provide an algorithm that $M$-guards a polygon using a convex decomposition of the polygon. We show that every point in the polygon is visible to at least four $2$-visibility guards and then extend the result to show that for any even $k \geq 2$ there exists a placement of guards such that every point in the polygon is visible to $k + 2$ guards.

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