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. © 2005 Elsevier B.V. All rights reserved.
Crossing-constrained hierarchical drawings / Finocchi, Irene. - In: JOURNAL OF DISCRETE ALGORITHMS. - ISSN 1570-8667. - 4:2(2006), pp. 299-312. [10.1016/j.jda.2005.06.001]
Crossing-constrained hierarchical drawings
FINOCCHI, Irene
2006
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. © 2005 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
