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A Distance Matrix Completion Approach to 1-Round Algorithms for Point Placement in the Plane

  • Md. Zamilur Rahman
  • Udayamoorthy Navaneetha Krishnan
  • Cory Jeane
  • Asish Mukhopadhyay
  • Yash P. Aneja
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10990)

Abstract

In this paper we propose a 1-round algorithm for approximate point placement in the plane in an adversarial model. The distance query graph presented to the adversary is chordal. The remaining distances are determined using a distance matrix completion algorithm for chordal graphs, based on a result by Bakonyi and Johnson [SIAM Journal on Matrix Analysis and Applications 16 (1995)]. The layout of the points is determined from the complete distance matrix in two ways: using the traditional Young-Householder approach as well as a Stochastic Proximity Embedding (SPE) method due to Agrafiotis [Journal of Computational Chemistry 24 (2003)].

Keywords

Distance geometry Point placement Distance matrix completion Embed algorithm Eigenvalue decomposition 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Md. Zamilur Rahman
    • 1
  • Udayamoorthy Navaneetha Krishnan
    • 1
  • Cory Jeane
    • 1
  • Asish Mukhopadhyay
    • 1
  • Yash P. Aneja
    • 2
  1. 1.School of Computer ScienceUniversity of WindsorWindsorCanada
  2. 2.Odette School of BusinessUniversity of WindsorWindsorCanada

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