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

Abstract

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(n 1 + ε) 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.KeywordsShort PathWork SpaceDual GraphSimple PathSimple PolygonThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.