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 named “controlled recursion” improves the time bound to O(n1+ε ) for any constant ε > 0. Second, we describe how to compute a shortest path between two points in a simple polygon. Although the shortest path problem in general graphs is NL-complete [11], this constrained problem can be solved in quadratic time using only constant work space.

• Type: Journal
• Year: 2010
• Where: WALCOM
• Authors: Tetsuo Asano, Wolfgang Mulzer, Yajun Wang
• Keywords: Algorithms, Constant Work Space, Shortest Path, WALCOM 2010, Work Space