Name
Abstract | ||
|---|---|---|
We study the computational complexity of the Hausdorff distance of two curves on the two-dimensional plane, in the context of the Turing machine-based complexity theory of real functions. It is proved that the Hausdorff distance of any two polynomial-time computable curves is a left-Σ2P real number. Conversely, for any tally set A in Σ2P, there exist two polynomial-time computable curves such that set A is computable in polynomial time relative to the Hausdorff distance of these two curves. More generally, we show that, for any set A in Σ2P, there exist two polynomial-time computable curves such that set A is computable in polynomial time relative to the Hausdorff distances of subcurves of these two curves. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.jco.2013.03.002 | Journal of Complexity |
Keywords | DocType | Volume |
Hausdorff distance,Computational complexity,Polynomial-time,Two-dimensional plane,Curves,Turing machine | Journal | 29 |
Issue | ISSN | Citations |
3 | 0885-064X | 0 |
PageRank | References | Authors |
0.34 | 6 | 1 |