Graph Drawing

Volume 8242 of the series Lecture Notes in Computer Science pp 484-495

Drawing Permutations with Few Corners

  • Sergey BeregAffiliated withDepartment of Computer Science, University of Texas at Dallas
  • , Alexander E. HolroydAffiliated withMicrosoft Research
  • , Lev NachmansonAffiliated withMicrosoft Research
  • , Sergey PupyrevAffiliated withDepartment of Computer Science, University of ArizonaInstitute of Mathematics and Computer Science, Ural Federal University

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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.