Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Coordinate representation of order types requires exponential storage
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Some provably hard crossing number problems
Discrete & Computational Geometry
Intersection graphs of segments
Journal of Combinatorial Theory Series B
Reasoning about Binary Topological Relations
SSD '91 Proceedings of the Second International Symposium on Advances in Spatial Databases
Recognizing string graphs in NP
Journal of Computer and System Sciences - STOC 2002
Journal of Computer and System Sciences - STOC 2001
Crossing number is hard for cubic graphs
Journal of Combinatorial Theory Series B
Crossing number of graphs with rotation systems
GD'07 Proceedings of the 15th international conference on Graph drawing
The complexity of several realizability problems for abstract topological graphs
GD'07 Proceedings of the 15th international conference on Graph drawing
Qualitative spatial reasoning with topological information
Qualitative spatial reasoning with topological information
Geometric intersection graph: do short cycles help?
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Integer representations of convex polygon intersection graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Sphere and dot product representations of graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Integer realizations of disk and segment graphs
Journal of Combinatorial Theory Series B
Data exchange with arithmetic operations
Proceedings of the 16th International Conference on Extending Database Technology
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We show that recognizing intersection graphs of convex sets has the same complexity as deciding truth in the existential theory of the reals. Comparing this to similar results on the rectilinear crossing number and intersection graphs of line segments, we argue that there is a need to recognize this level of complexity as its own class.