Constant-Work-Space Algorithm for a Shortest Path in a Simple Polygon

We present two space-efficient algorithms. First, we show how to report a simple path between two arbitrary nodes in a given tree. Using a technique called “computing instead of storing”, we can design a naive quadratic-time algorithm for the problem using only constant work space, i.e., O(log n) bits in total for the work space, where n is the number of nodes in the tree. Then, another technique “controlled recursion” improves the time bound to O(n) for any positive constant ε. Second, we describe how to compute a shortest path between two points in a simple n-gon. Although the shortest path problem in general graphs is NL-complete, this constrained problem can be solved in quadratic time using only constant work space.