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

  • Tetsuo Asano
  • Wolfgang Mulzer
  • Yajun Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)


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.


Short Path Work Space Dual Graph Simple Path Simple Polygon 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tetsuo Asano
    • 1
  • Wolfgang Mulzer
    • 2
  • Yajun Wang
    • 3
  1. 1.School of Information ScienceJAISTJapan
  2. 2.Department of Computer SciencePrinceton UniversityUSA
  3. 3.Microsft ResearchBeijingChina

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