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We prove that every simply connected orthogonal polygon of $n$ vertices canbe partitioned into $\left\lfloor\frac{3 n +4}{16}\right\rfloor$ (simplyconnected) orthogonal polygons of at most 8 vertices. It yields a new andshorter proof of the theorem of A. Aggarwal that $\left\lfloor\frac{3 n+4}{16}\right\rfloor$ mobile guards are sufficient to control the interior ofan $n$-vertex orthogonal polygon. Moreover, we strengthen this result byrequiring combinatorial guards (visibility is only required at the endpoints ofpatrols) and prohibiting intersecting patrols. This yields positive answers totwo questions of O'Rourke. Our result is also a further example of the"metatheorem" that (orthogonal) art gallery theorems are based on partitiontheorems.

Partitioning orthogonal polygons into at most 8-vertex pieces, with application to an art gallery theorem