Abstract
The fortress problemwas posed independently by Joseph Malkelvitch and Derick Wood to determine the number of guards sufficient to cover the exterior of an n-vertex polygon. O'Rourke and Wood showed that \( \lceil n/2 \rceil \) vertex guards are sometimes necessary and always sufficient. Yiu and Choi considered a variation of the problem by allowing each guard to patrol an edge (called an edge guard) of the polygon and obtained a tight bound of \( \lceil n/3 \rceil \) edge guards for general polygons. In this paper, we unify and generalize both results by considering the number of k-consecutive vertex guards that are required to solve the fortress problem. A tight bound of \( \lceil n/(k+1) \rceil \) is obtained.
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