Planar Drawings of Fixed-Mobile Bigraphs

  • Michael A. Bekos
  • Felice De Luca
  • Walter DidimoEmail author
  • Tamara Mchedlidze
  • Martin Nöllenburg
  • Antonios Symvonis
  • Ioannis G. Tollis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10692)


A fixed-mobile bigraph G is a bipartite graph such that the vertices of one partition set are given with fixed positions in the plane and the mobile vertices of the other part, together with the edges, must be added to the drawing. We assume that G is planar and study the problem of finding, for a given \(k \ge 0\), a planar poly-line drawing of G with at most k bends per edge. In the most general case, we show NP-hardness. For \(k=0\) and under additional constraints on the positions of the fixed or mobile vertices, we either prove that the problem is polynomial-time solvable or prove that it belongs to NP. Finally, we present a polynomial-time testing algorithm for a certain type of “layered” 1-bend drawings.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Michael A. Bekos
    • 1
  • Felice De Luca
    • 2
  • Walter Didimo
    • 2
    Email author
  • Tamara Mchedlidze
    • 3
  • Martin Nöllenburg
    • 4
  • Antonios Symvonis
    • 5
  • Ioannis G. Tollis
    • 6
  1. 1.University of TübingenTübingenGermany
  2. 2.Università degli Studi di PerugiaPerugiaItaly
  3. 3.Karlsruhe Institute of TechnologyKarlsruheGermany
  4. 4.TU WienViennaAustria
  5. 5.National Technical University of AthensAthensGreece
  6. 6.University of CreteHeraklionGreece

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