Noncrossing subgraphs in topological layouts
SIAM Journal on Discrete Mathematics
String graphs. II.: Recognizing string graphs is NP-hard
Journal of Combinatorial Theory Series B
Approximations for the maximum acyclic subgraph problem
Information Processing Letters
Journal of the ACM (JACM)
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Technique for Drawing Directed Graphs
IEEE Transactions on Software Engineering
Crossing Number of Abstract Topological Graphs
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Crossing minimization in weighted bipartite graphs
Journal of Discrete Algorithms
A fast and simple heuristic for constrained two-level crossing reduction
GD'04 Proceedings of the 12th international conference on Graph Drawing
Approximating the maximum sharing problem
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Crossing-constrained hierarchical drawings
Journal of Discrete Algorithms
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We study the problem of producing hierarchical drawings of layered graphs when some pairs of edges are not allowed to cross.W e 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.