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Planar spanners and approximate shortest path queries among obstacles in the plane

  • Srinivasa Arikati
  • Danny Z. Chen
  • L. Paul Chew
  • Gautam Das
  • Michiel Smid
  • Christos D. Zaroliagis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)

Abstract

We consider the problem of finding an obstacle-avoiding path between two points s and t in the plane, amidst a set of disjoint polygonal obstacles with a total of n vertices. The length of this path should be within a small constant factor c of the length of the shortest possible obstacle-avoiding s-t path measured in the L p -metric. Such an approximate shortest path is called a c-short path, or a short path with stretch factor c. The goal is to preprocess the obstacle-scattered plane by creating an efficient data structure that enables fast reporting of a c-short path (or its length). In this paper, we give a family of algorithms for the above problem that achieve an interesting trade-off between the stretch factor, the query time and the preprocessing bounds. Our main results are algorithms that achieve logarithmic length query time, after subquadratic time and space preprocessing.

Keywords

Short Path Planar Graph Short Path Problem Path Query Short Path Tree 
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 1996

Authors and Affiliations

  • Srinivasa Arikati
    • 1
  • Danny Z. Chen
    • 2
  • L. Paul Chew
    • 3
  • Gautam Das
    • 1
  • Michiel Smid
    • 4
  • Christos D. Zaroliagis
    • 5
  1. 1.Math Sciences DeptThe University of MemphisMemphisUSA
  2. 2.Dept of Computer Sc. and EngUniv. of Notre DameNotre DameUSA
  3. 3.Dept of Computer ScCornell UniversityIthacaUSA
  4. 4.Dept of Computer ScKing's College LondonLondonUK
  5. 5.Max-Planck-Institut für InformatikSaarbrückenGermany

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