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On the complexity of approximating Euclidean traveling salesman tours and minimum spanning trees

  • Gautam Das
  • Sanjiv Kapoor
  • Michiel Smid
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1180)

Abstract

We consider the problems of computing r-approximate traveling salesman tours and r-approximate minimum spanning trees for a set of n points in ℝd, where d≥ 1 is a constant. In the algebraic computation tree model, the complexities of both these problems are shown to be θ(nlog(n/r)), for all n and r such that r<n and r is larger than some constant. In the more powerful model of computation that additionally uses the floor function and random access, both problems can be solved in O(n) time if r=θ(n 1−1/d ).

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Gautam Das
    • 1
  • Sanjiv Kapoor
    • 2
  • Michiel Smid
    • 3
  1. 1.Math Sciences Dept.The University of MemphisMemphisUSA
  2. 2.Department of Computer ScienceIndian Institute of TechnologyNew DelhiIndia
  3. 3.Department of Computer ScienceKing's College LondonLondonUK

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