Geometric optimization and the polynomial hierarchy

  • Chanderjit Bajaj
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 206)


We illustrate two different techniques of accurately classifying geometric optimization problems in the polynomial hierarchy. We show that if NP≠Co-NP then there are interesting natural geometric optimization problems (location-allocation problems under minsum) in △ 2 P that are in neither NP nor Co-NP. Hence, all these problems are shown to belong properly to △ 2 P , the second level of the polynomial hierarchy. We also show that if NP≠Co-NP then there are again some interesting geometric optimization problems (location-allocation problems under minmax), properly in △ 2 P and furthermore they are complete for a class DP (which is contained in △ 2 P and contains NP Co-NP).


Distance Metrics Destination Point Polynomial Hierarchy Exact Cover Turing Reduction 
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 1985

Authors and Affiliations

  • Chanderjit Bajaj
    • 1
  1. 1.Department of Computer SciencePurdue UniversityWest Lafayette

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