Yiming Wang, Sergiy Butenko, The two-guard problem on curvininear polygons

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DOI: 10.23952/jnva.9.2025.1.01

Volume 9, Issue 1, 1 February 2025, Pages 1-14

Abstract. Given a simple polygon on the plane with two distinct vertices, s and t, the original two-guard problem asks whether there is a route for two guards to simultaneously walk along the two boundary chains from s to t so that they are always mutually visible. We study a generalization of this problem to curvilinear polygons, in which the boundary consists of a finite number of curved pieces. We focus on locally-convex polygons, which are polygons with locally convex arcs, and we solve this problem in $\mathcal{O}(n^2)$ time for a curvilinear polygon with n edges, by either constructing a required route or deciding that such route does not exist.

How to Cite this Article:
Y. Wang, S. Butenko, The two-guard problem on curvininear polygons, J. Nonlinear Var. Anal. 9 (2025), 1-14.