Drawing Permutations with Few Corners

  • Sergey Bereg
  • Alexander E. Holroyd
  • Lev Nachmanson
  • Sergey Pupyrev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)


A permutation may be represented by a collection of paths in the plane. We consider a natural class of such representations, which we call tangles, in which the paths consist of straight segments at 45 degree angles, and the permutation is decomposed into nearest-neighbour transpositions. We address the problem of minimizing the number of crossings together with the number of corners of the paths, focusing on classes of permutations in which both can be minimized simultaneously. We give algorithms for computing such tangles for several classes of permutations.


Minimal Pair Identity Permutation Sorting Network Integrate Circuit Design Vertical Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Sergey Bereg
    • 1
  • Alexander E. Holroyd
    • 2
  • Lev Nachmanson
    • 2
  • Sergey Pupyrev
    • 3
    • 4
  1. 1.Department of Computer ScienceUniversity of Texas at DallasUSA
  2. 2.Microsoft ResearchUSA
  3. 3.Department of Computer ScienceUniversity of ArizonaUSA
  4. 4.Institute of Mathematics and Computer ScienceUral Federal UniversityRussia

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