Acta Informatica

, Volume 42, Issue 6–7, pp 419–428 | Cite as

Embedding linear orders in grids

  • Andrzej Ehrenfeucht
  • Tero HarjuEmail author
  • Grzegorz Rozenberg
Original Article


A grid (or a mesh) is a two-dimensional permutation: an m× n-grid of size mn is an m× n-matrix where the entries run through the elements {1,2, …, mn}. We prove that if δ1 and δ2 are any two linear orders on {1,2, …, N}, then they can be simultaneously embedded (in a well defined sense) into a unique grid having the smallest size.


Linear Order Comparability Graph Order Preserve Permutation Graph Compatible Pair 
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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Andrzej Ehrenfeucht
    • 1
  • Tero Harju
    • 2
    Email author
  • Grzegorz Rozenberg
    • 1
    • 3
  1. 1.Department of Computer ScienceUniversity of Colorado at BoulderBoulderUSA
  2. 2.Department of MathematicsUniversity of TurkuTurkuFinland
  3. 3.Leiden Institute for Advanced Computer ScienceLeiden UniversityLeidenThe Netherlands

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