25 citations · 112 across the 30 of their papers we have counts for
8 papers · 1 filter
Minimizing Visible Edges in Polyhedra
Csaba D. Tóth, Jorge Urrutia, Giovanni Viglietta
We prove that, given a polyhedron in , every point in that does not see any vertex of must see eight or more edges of $\mathca…
Chasing Puppies: Mobile Beacon Routing on Closed Curves
Mikkel Abrahamsen, Jeff Erickson, Irina Kostitsyna +5
We solve an open problem posed by Michael Biro at CCCG 2013 that was inspired by his and others' work on beacon-based routing. Consider a human and a puppy on a simple closed curve…
Optimally Guarding 2-Reflex Orthogonal Polyhedra by Reflex Edge Guards
Giovanni Viglietta
Let an orthogonal polyhedron be the union of a finite set of boxes in (i.e., cuboids with edges parallel to the coordinate axes), whose surface is a connected 2-manif…
The Shadows of a Cycle Cannot All Be Paths
Prosenjit Bose, Jean-Lou De Carufel, Michael G. Dobbins +2
A "shadow" of a subset of Euclidean space is an orthogonal projection of into one of the coordinate hyperplanes. In this paper we show that it is not possible for all three…
Face-Guarding Polyhedra
Giovanni Viglietta
We study the Art Gallery Problem for face guards in polyhedral environments. The problem can be informally stated as: how many (not necessarily convex) windows should we place on t…
Guarding and Searching Polyhedra
Giovanni Viglietta
We tackle the Art Gallery Problem and the Searchlight Scheduling Problem in 3-dimensional polyhedral environments, putting special emphasis on edge guards and orthogonal polyhedra.
Partial Searchlight Scheduling is Strongly PSPACE-Complete
Giovanni Viglietta
The problem of searching a polygonal region for an unpredictably moving intruder by a set of stationary guards, each carrying an orientable laser, is known as the Searchlight Sched…
Searching Polyhedra by Rotating Half-Planes
Giovanni Viglietta
The Searchlight Scheduling Problem was first studied in 2D polygons, where the goal is for point guards in fixed positions to rotate searchlights to catch an evasive intruder. Here…