On Guarding Orthogonal Polygons with Bounded Treewidth

TL;DR

This paper demonstrates that various orthogonal polygon guarding problems become efficiently solvable in polygons with bounded treewidth by leveraging graph algorithms, significantly improving computational feasibility.

Contribution

It introduces a unified approach to solve multiple guarding problems in orthogonal polygons with bounded treewidth using graph algorithms.

Findings

Guarding problems are solvable in linear time for polygons with bounded treewidth.

The approach applies to multiple guarding models, including rectangular, staircase, and orthogonal path guards.

The method leverages existing algorithms for graphs of bounded treewidth.

Abstract

There exist many variants of guarding an orthogonal polygon in an orthogonal fashion: sometimes a guard can see an entire rectangle, or along a staircase, or along an orthogonal path with at most $k$ bends. In this paper, we study all these guarding models in the special case of orthogonal polygons that have bounded treewidth in some sense. Exploiting algorithms for graphs of bounded treewidth, we show that the problem of finding the minimum number of guards in these models becomes linear-time solvable in orthogonal polygons of bounded treewidth.