Crossing-constrained hierarchical drawings

Authors:
Irene Finocchi
Affiliations:
Dipartimento di Informatica, Universití degli Studi di Roma "La Sapienza", Via Salaria 113, 00198 Rome, Italy
Venue:
Journal of Discrete Algorithms
Year:
2006

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Abstract

We study the problem of computing hierarchical drawings of layered graphs when some pairs of edges are not allowed to cross. We show that deciding the existence of a drawing satisfying at least k non-crossing constraints from a given set is NP-hard, even if the graph is 2-layered and even when the permutation of the vertices on one side of the bipartition is fixed. We then propose simple constant-ratio approximation algorithms for the optimization version of the problem, which requires to find a maximum realizable subset of constraints, and we discuss how to extend the well-known hierarchical approach for creating layered drawings of directed graphs so as to minimize the number of edge crossings while maximizing the number of satisfied constraints.