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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)

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.

Keywords

Short Path Work Space Dual Graph Simple Path Simple Polygon 
These 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.

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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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