Witness Set for simple polygons is in NP ∩ XP and admits an n^{f(k)}-time algorithm via combinatorial discretization, in contrast to its ∃R-complete dual.
International Journal of Computational Geometry and Application22(03), 187–205 (2012)
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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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Witness Set: A Visibility Problem in $NP\cap XP$
Witness Set for simple polygons is in NP ∩ XP and admits an n^{f(k)}-time algorithm via combinatorial discretization, in contrast to its ∃R-complete dual.
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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.