Linear time algorithms for visibility and shortest path problems inside simple polygons
SCG '86 Proceedings of the second annual symposium on Computational geometry
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
An optimal algorithm for the two-guard problem
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
An algorithm for searching a polygonal region with a flashlight
Proceedings of the sixteenth annual symposium on Computational geometry
Sweeping simple polygons with a chain of guards
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On Computing Connected Components of Line Segments
IEEE Transactions on Computers
A linear-time algorithm for finding all door locations that make a room searchable
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
A characterization of polygonal regions searchable from the boundary
IJCCGGT'03 Proceedings of the 2003 Indonesia-Japan joint conference on Combinatorial Geometry and Graph Theory
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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.