  We examine the Art Gallery Problem with Edge Guards. We present a heuristic
algorithm to arrange edge guards to guard only the inward side of the walls of
any N-vertex simple polygonal gallery using at most roof (N/4) edge guards - a
weakened version of Toussaint's conjecture on the number of edge guards that
can guard an entire simple polygon. Our study indicates that solving this
weaker problem could give a handle on the full problem.
