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. We 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.
Layered drawings of graphs with crossing constraints / Finocchi, Irene. - Proc. of the 7th Annual Int. Computing and Combinatorics Conference (COCOON'01), (2001), pp. 357-367. (7th Annual International Conference on Computing and Combinatorics, GUILIN, PEOPLES R CHINA, AUG 20-23, 2001). [10.1007/3-540-44679-6_39].
Layered drawings of graphs with crossing constraints
Irene Finocchi
2001
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. We 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.
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