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A universal algorithm for finding the shortest distance between systems of points.

Igor A Blatov1, Elena V Kitaeva2, Alexander P Shevchenko2

  • 1Volga State University of Telecommunications and Informatics, Moskovskoe sh. 77, Samara, 443010, Russian Federation.

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Three new algorithms efficiently compare geometrical arrangements of 3D points. The best method, combining Hungarian and Kabsch algorithms, accurately analyzes chemical structures like ligands and nets with hundreds of points.

Keywords:
algorithmsshortest distancesystems of points

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Area of Science:

  • Computational geometry
  • Cheminformatics
  • Structural analysis

Background:

  • Comparing geometric structures is crucial in various scientific fields.
  • Existing algorithms have limitations in speed and accuracy for complex datasets.
  • Efficient methods are needed for analyzing molecular and crystalline structures.

Purpose of the Study:

  • To propose universal algorithms for geometrical comparison of point sets in 3D Euclidean space.
  • To analyze the efficiency and accuracy of these algorithms.
  • To apply the developed algorithms to chemical object comparison.

Main Methods:

  • Development of three novel algorithms for geometrical comparison of n-point sets in R³.
  • Theoretical analysis of algorithm efficiency, proving an upper bound of O(n³/ε³/²).
  • Integration and enhancement of the Hungarian and Kabsch algorithms for improved performance.

Main Results:

  • All proposed algorithms achieve an efficiency bound of O(n³/ε³/²).
  • The most effective algorithm demonstrates speed suitable for hundreds of points.
  • Successful application to compare finite (ligands) and periodic (nets) chemical objects.

Conclusions:

  • The developed algorithms provide efficient and accurate geometrical comparisons for 3D point sets.
  • The enhanced Hungarian-Kabsch algorithm offers a robust solution for analyzing chemical structures.
  • These methods advance the field of structural comparison in computational chemistry and related areas.