Finding the k-Visibility Region of a Point in a Simple Polygon in the Memory-Constrained Model

We study the problem of k-visibility in the memoryconstrained model. In this model, the input resides in a randomly accessible read-only memory of O(n) words with O(log n) bits each. An algorithm can read and write O(s) additional words of workspace during its execution, and it writes its output to write-only memory. In a given polygon P , for a given point q ∈ P , we say a point p is inside the k-visibility region of q iff the segment pq intersects the boundary of P at most k times. Given a simple n-vertex polygon P stored in a read-only array and a point q ∈ P , we give a time-space trade-off algorithm which reports a suitable representation of the k-visibility region of q in O(n/s+n log s) time usingO(s) words of workspace.