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Algorithmica

, Volume 81, Issue 9, pp 3464–3493 | Cite as

NodeTrix Planarity Testing with Small Clusters

  • Emilio Di Giacomo
  • Giuseppe Liotta
  • Maurizio Patrignani
  • Ignaz Rutter
  • Alessandra TappiniEmail author
Article
  • 36 Downloads

Abstract

We study the NodeTrix planarity testing problem for flat clustered graphs when the maximum size of each cluster is bounded by a constant k. We consider both the case when the sides of the matrices to which the edges are incident are fixed and the case when they can be chosen arbitrarily. We show that NodeTrix planarity testing with fixed sides can be solved in \(O(k^{3k+\frac{3}{2}} \cdot n)\) time for every flat clustered graph that can be reduced to a partial 2-tree by collapsing its clusters into single vertices. In the general case, NodeTrix planarity testing with fixed sides can be solved in O(n) time for \(k = 2\), but it is NP-complete for any \(k > 2\). NodeTrix planarity testing remains NP-complete also in the free sides model when \(k > 4\).

Keywords

NodeTrix Hybrid representation Hybrid planarity Graph drawing 

Notes

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Authors and Affiliations

  1. 1.Università degli Studi di PerugiaPerugiaItaly
  2. 2.Roma Tre UniversityRomaItaly
  3. 3.University of PassauPassauGermany

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