5 papers
Pursuit-Evasion in Graphs: Zombies, Lazy Zombies and a Survivor
Prosenjit Bose, Jean-Lou De Carufel, Thomas Shermer
We study zombies and survivor, a variant of the game of cops and robber on graphs. In this variant, the single survivor plays the role of the robber and attempts to escape from the…
An Efficient Algorithm for the Proximity Connected Two Center Problem
Binay Bhattacharya, Amirhossein Mozafari, Thomas C. Shermer
Given a set of points in the plane, the -center problem is to find congruent disks of minimum possible radius such that their union covers all the points in . The…
Gathering by Repulsion
Prosenjit Bose, Thomas Shermer
We consider a repulsion actuator located in an -sided convex environment full of point particles. When the actuator is activated, all the particles move away from the actuator.…
A Combinatorial Bound for Beacon-based Routing in Orthogonal Polygons
Thomas C. Shermer
Beacon attraction is a movement system whereby a robot (modeled as a point in 2D) moves in a free space so as to always locally minimize its Euclidean distance to an activated beac…
Unit Rectangle Visibility Graphs
Alice Dean, Joanna A. Ellis-Monaghan, Sarah Hamilton +1
Over the past twenty years, rectangle visibility graphs have generated considerable interest, in part due to their applicability to VLSI chip design. Here we study unit rectangle v…