Computer aided layout of entity relationship diagrams
Journal of Systems and Software - Special double issue on the entity-relationship approach to databases and related software
Separating and nonseparating disjoint homotopic cycles in graph embeddings
Journal of Combinatorial Theory Series B
A Linear Time Algorithm for Embedding Graphs in an Arbitrary Surface
SIAM Journal on Discrete Mathematics
Improved approximations of crossings in graph drawings
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Drawings of Cm × Cn with one disjoint family II
Journal of Combinatorial Theory Series B
Computing crossing numbers in quadratic time
Journal of Computer and System Sciences - STOC 2001
Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Crossing number is hard for cubic graphs
Journal of Combinatorial Theory Series B
Computing crossing number in linear time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The crossing number of K11 is 100
Journal of Graph Theory
Improved upper bounds on the crossing number
Proceedings of the twenty-fourth annual symposium on Computational geometry
A New Approach to Exact Crossing Minimization
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Inserting a vertex into a planar graph
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximating the Crossing Number of Apex Graphs
Graph Drawing
On the crossing number of almost planar graphs
GD'06 Proceedings of the 14th international conference on Graph drawing
Approximating the crossing number of toroidal graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Planar crossing numbers of genus g graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Adding one edge to planar graphs makes crossing number hard
Proceedings of the twenty-sixth annual symposium on Computational geometry
An algorithm for the graph crossing number problem
Proceedings of the forty-third annual ACM symposium on Theory of computing
A tighter insertion-based approximation of the crossing number
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Facets in the Crossing Number Polytope
SIAM Journal on Discrete Mathematics
Vertex insertion approximates the crossing number of apex graphs
European Journal of Combinatorics
On graph crossing number and edge planarization
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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The crossing number of a graph is the least number of pairwise edge crossings in a drawing of the graph in the plane. We provide an O(n log n) time constant factor approximation algorithm for the crossing number of a graph of bounded maximum degree which is "densely enough" embeddable in an arbitrary fixed orientable surface. Our approach combines some known tools with a powerful new lower bound on the crossing number of an embedded graph. This result extends previous results that gave such approximations in particular cases of projective, toroidal or apex graphs; it is a qualitative improvement over previously published algorithms that constructed low-crossing-number drawings of embeddable graphs without giving any approximation guarantees. No constant factor approximation algorithms for the crossing number problem over comparably rich classes of graphs are known to date.