TY - JOUR
T1 - Scandinavian thins on top of cake : new and improved algorithms for stacking and packing
AU - Alt, H.
AU - Arkin, E.M.
AU - Efrat, A.
AU - Hart, G.
AU - Hurtado, Ferran
AU - Kostitsyna, I.
AU - Kröller, A.
AU - Mitchell, J.S.B.
AU - Polishchuk, V.
PY - 2014
Y1 - 2014
N2 - We show how to compute the smallest rectangle that can enclose any polygon, from a given set of polygons, in nearly linear time; we also present a PTAS for the problem, as well as a linear-time algorithm for the case when the polygons are rectangles themselves. We prove that finding a smallest convex polygon that encloses any of the given polygons is NP-hard, and give a PTAS for minimizing the perimeter of the convex enclosure. We also give efficient algorithms to find the smallest rectangle simultaneously enclosing a given pair of convex polygons.
AB - We show how to compute the smallest rectangle that can enclose any polygon, from a given set of polygons, in nearly linear time; we also present a PTAS for the problem, as well as a linear-time algorithm for the case when the polygons are rectangles themselves. We prove that finding a smallest convex polygon that encloses any of the given polygons is NP-hard, and give a PTAS for minimizing the perimeter of the convex enclosure. We also give efficient algorithms to find the smallest rectangle simultaneously enclosing a given pair of convex polygons.
U2 - 10.1007/s00224-013-9493-9
DO - 10.1007/s00224-013-9493-9
M3 - Article
SN - 1432-4350
VL - 54
SP - 689
EP - 714
JO - Theory of Computing Systems
JF - Theory of Computing Systems
IS - 4
ER -