article

The algebraic degree of geometric optimization problems

Author:

Chanderjit BajajAuthors Info & Claims

Discrete & Computational Geometry, Volume 3, Issue 2

Pages 177 - 191

https://doi.org/10.1007/BF02187906

Published: 01 December 1988 Publication History

Abstract

In this paper we apply Galois methods to certain fundamentalgeometric optimization problems whose exact computational complexity has been an open problem for a long time. In particular we show that the classic Weber problem, along with theline-restricted Weber problem and itsthree-dimensional version are in general not solvable by radicals over the field of rationals. One direct consequence of these results is that for these geometric optimization problems there existsno exact algorithm under models of computation where the root of an algebraic equation is obtained using arithmetic operations and the extraction ofkth roots. This leaves only numerical or symbolic approximations to the solutions, where the complexity of the approximations is shown to be primarily a function of the algebraic degree of the optimum solution point.

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Index Terms

The algebraic degree of geometric optimization problems
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on polynomials
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
  2. Randomness, geometry and discrete structures
    1. Computational geometry

Index terms have been assigned to the content through auto-classification.

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cover image Discrete & Computational Geometry

Discrete & Computational Geometry Volume 3, Issue 2

June 1988

95 pages

ISSN:0179-5376

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Copyright © Copyright © 1988 Springer-Verlag New York Inc.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 1988

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Lindheim J(2023)Simple approximative algorithms for free-support Wasserstein barycentersComputational Optimization and Applications10.1007/s10589-023-00458-385:1(213-246)Online publication date: 1-Mar-2023
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