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(logn) 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(n1+e) for any positive constant e. 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.

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