Some complexity issues on the simply connected regions of the two-dimensional plane
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A polynomial-time computable curve whose interior has a nonrecursive measure
Theoretical Computer Science
Computational Complexity of Two-Dimensional Regions
SIAM Journal on Computing
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Theoretical Computer Science - Special issue on computability and complexity in analysis
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FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Jordan Curves with Polynomial Inverse Moduli of Continuity
Electronic Notes in Theoretical Computer Science (ENTCS)
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Electronic Notes in Theoretical Computer Science (ENTCS)
On the Complexity of Convex Hulls of Subsets of the Two-Dimensional Plane
Electronic Notes in Theoretical Computer Science (ENTCS)
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Electronic Notes in Theoretical Computer Science (ENTCS)
Information and Computation
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Jordan curves can be used to represent special subsets of the Euclidean plane, either the (open) interior of the curve or the (compact) union of the interior and the curve itself. We compare the latter with other representations of compact sets using grids of points and we are able to show that knowing the length of a rectifiable curve is sufficient to translate from the grid representation to the Jordan curve.