Fast Node Overlap Removal

  • Tim Dwyer
  • Kim Marriott
  • Peter J. Stuckey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)


The problem of node overlap removal is to adjust the layout generated by typical graph drawing methods so that nodes of non-zero width and height do not overlap, yet are as close as possible to their original positions. We give an O(n log n) algorithm for achieving this assuming that the number of nodes overlapping any single node is bounded by some constant. This method has two parts, a constraint generation algorithm which generates a linear number of “separation” constraints and an algorithm for finding a solution to these constraints “close” to the original node placement values. We also extend our constraint solving algorithm to give an active set based algorithm which is guaranteed to find the optimal solution but which has considerably worse theoretical complexity. We compare our method with convex quadratic optimization and force scan approaches and find that it is faster than either, gives results of better quality than force scan methods and similar quality to the quadratic optimisation approach.


graph layout constrained optimization separation constraints 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tim Dwyer
    • 1
  • Kim Marriott
    • 1
  • Peter J. Stuckey
    • 2
  1. 1.School of Comp. Science & Soft. Eng.Monash UniversityAustralia
  2. 2.NICTA Victoria Laboratory Dept. of Comp. Science & Soft. Eng.University of MelbourneAustralia

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