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Layered Drawings of Graphs with Crossing Constraints

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Computing and Combinatorics (COCOON 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2108))

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Abstract

We study the problem of producing hierarchical drawings of layered graphs when some pairs of edges are not allowed to cross.We show that deciding on the existence of a drawing satisfying at least k constraints from a given set of non-crossing constraints is NP-complete even if the graph is 2-layered and even when the permutation of the vertices on one side of the bipartition is fixed.W e also propose simple constant-ratio approximation algorithms for the optimization version of the problem and we discuss how to extend the well-known hierarchical approach for creating layered drawings of directed graphs with the capability of minimizing the number of edge crossings while maximizing the number of satisfied non-crossing constraints.

Work supported in part by the project “Algorithms for Large Data Sets: Science and Engineering” of the Italian Ministry of University and of Scientific and Technological Research (MURST 40%).

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Rome “La Sapienza”, Rome

    Irene Finocchi

Authors
  1. Irene Finocchi
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Massachusetts, One University Avenue, Lowell, MA, 01854, USA

    Jie Wang

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© 2001 Springer-Verlag Berlin Heidelberg

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Finocchi, I. (2001). Layered Drawings of Graphs with Crossing Constraints. In: Wang, J. (eds) Computing and Combinatorics. COCOON 2001. Lecture Notes in Computer Science, vol 2108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44679-6_39

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  • DOI: https://doi.org/10.1007/3-540-44679-6_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42494-9

  • Online ISBN: 978-3-540-44679-8

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