  We are interested in the problem of guarding simple orthogonal polygons with
the minimum number of $ r $-guards. The interior point $ p $ belongs an
orthogonal polygon $ P $ is visible from $ r $-guard $ g $, if the minimum area
rectangle contained $ p $ and $ q $ lies within $ P $. A set of point guards in
polygon $ P $ is named guard set (as denoted $ G $) if the union of visibility
areas of these point guards be equal to polygon $ P $ i.e. every point in $ P $
be visible from at least one point guards in $ G $. For an orthogonal polygon,
if dual graph of vertical decomposition is a path, it is named path polygon. In
this paper, we show that the problem of finding the minimum number of $ r
$-guards (minimum guard set) becomes linear-time solvable in orthogonal path
polygons. The path polygon may have dent edges in every four orientations. For
this class of orthogonal polygon, the problem has been considered by Worman and
Keil who described an algorithm running in $ O(n^{17} poly\log n) $-time where
$ n $ is the size of the input polygon. The problem of finding minimum number
of guards for simple polygon with general visibility is NP-hard, even if
polygon be orthogonal. Our algorithm is purely geometric and presents a new
strategy for $ r $-guarding orthogonal polygons and guards can be placed
everywhere in the interior and boundary of polygon.
