Computing a visibility polygon using few variables

We present several algorithms for computing the visibility polygon of a simple polygon PP of n vertices (out of which r   are reflex) from a viewpoint inside PP, when PP resides in read-only memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in O(nr¯) time, where r¯ denotes the number of reflex vertices of PP that are part of the output. Whenever we are allowed to use O(s)O(s) variables, the running time decreases to O(nr2s+nlog2r) (or O(nr2s+nlogr) randomized expected time), where s∈O(logr). This is the first algorithm in which an exponential space-time trade-off for a geometric problem is obtained.