No l Grid-Points in Spaces of Small Dimension

  • Hanno Lefmann
Conference paper

DOI: 10.1007/978-3-540-68880-8_25

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5034)
Cite this paper as:
Lefmann H. (2008) No l Grid-Points in Spaces of Small Dimension. In: Fleischer R., Xu J. (eds) Algorithmic Aspects in Information and Management. AAIM 2008. Lecture Notes in Computer Science, vol 5034. Springer, Berlin, Heidelberg

Abstract

Motivated by a question raised by Pór and Wood in connection with compact embeddings of graphs in \({\mathbb Z}^d\), we investigate generalizations of the no-three-in-line-problem. For several pairs (k,l) we give algorithmic lower, and upper bounds on the largest sizes of subsets S of grid-points from the d-dimensional T × ⋯ ×T-grid, where no l distinct grid-points of S are contained in a k-dimensional affine or linear subspace.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hanno Lefmann
    • 1
  1. 1.Fakultät für InformatikTU ChemnitzChemnitzGermany

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