Generalized guarding and partitioning for rectilinear polygons

Generalized Guarding and Partitioning for Rectilinear Polygons

Guarding Fat Polygons and Triangulating Guarded Polygons

In this paper we study three related problems: (i) Given a fat polygon P , we show how to find a set G of points in P such that every point on the boundary of P sees at least one point of G. The set G is said to guard the boundary of P and its cardinality depends on the shape parameters of P . Fat polygons are often used to model more realistic inputs. (ii) Given k points that guard the boundar...

Fast Vertex Guarding for Polygons

For a polygon P with n vertices, the vertex guarding problem asks for the minimum subset G of P ’s vertices such that every point in P is seen by at least one point in G. This problem is NP-complete and APX-hard. The first approximation algorithm (Ghosh, 1987) involves decomposing P into O ( n ) cells that are equivalence classes for visibility from the vertices of P . This discretized problem ...

Triangulating and Guarding Realistic Polygons

We propose a new model of realistic input: k-guardable objects. An object is k-guardable if its boundary can be seen by k guards in the interior of the object. In this abstract, we describe a simple algorithm for triangulating k-guardable polygons. Our algorithm, which is easily implementable, takes linear time assuming that k is constant.

On k-Guarding Polygons

We describe a polynomial time O(k log log OPTk(P ))approximation algorithm for the k-guarding problem of finding a minimum number, OPTk(P ), of vertex guards of an n-vertex simple polygon P so that for every point p ∈ P , the number of guards that see p is at least the minimum of k and the number of vertices that see p. Our approach finds O ( k ε log log 1 ε ) size (k, ε)-nets for instances of ...