Order type realizability, ∃R-complete in the worst case, can be decided in expected NP time under smoothed analysis.
Journal of Symbolic Computation5(1–2), 37–64 (1988)
2 Pith papers cite this work. Polarity classification is still indexing.
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Linkage realization in polygonal domains is W[1]-hard parameterized by graph size and NP-hard for paths with prescribed endpoints, with a linear-time algorithm for short paths in convex polygons.
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Smoothed Analysis of Order Types
Order type realizability, ∃R-complete in the worst case, can be decided in expected NP time under smoothed analysis.
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Realizing Planar Linkages in Polygonal Domains
Linkage realization in polygonal domains is W[1]-hard parameterized by graph size and NP-hard for paths with prescribed endpoints, with a linear-time algorithm for short paths in convex polygons.