Hide-and-Seek: Algorithms for Polygon Walk Problems

Jack and Jill want to play hide-and-seek on the boundary of a simple polygon. Given arbitrary paths for the two children along this boundary, our goal is to determine whether Jack can walk along his path without ever being seen by Jill. To solve this problem, we use a linear-sized skeleton invisibility diagram to implicitly represent invisibility information between pairs of points on the boundary of the simple polygon. This structure has additional applications for any polygon walk problem where one entity wishes to remain hidden throughout a traversal of some path. We also show how Jack can avoid being seen not just by one moving child but by an arbitrary number of moving children.