10 research outputs found
Corrigendum to:Approximating minimum-area rectangular and convex containers for packing convex polygons
This note corrects an error in the paper “Approximating minimum-area rectangular and convex containers for packing convex polygons”, which appeared in JoCG, Vol. 8(1), pages 1–10.</p
Approximating Smallest Containers for Packing Three-dimensional Convex Objects
We investigate the problem of computing a minimal-volume container for the
non-overlapping packing of a given set of three-dimensional convex objects.
Already the simplest versions of the problem are NP-hard so that we cannot
expect to find exact polynomial time algorithms. We give constant ratio
approximation algorithms for packing axis-parallel (rectangular) cuboids under
translation into an axis-parallel (rectangular) cuboid as container, for
cuboids under rigid motions into an axis-parallel cuboid or into an arbitrary
convex container, and for packing convex polyhedra under rigid motions into an
axis-parallel cuboid or arbitrary convex container. This work gives the first
approximability results for the computation of minimal volume containers for
the objects described
Improved Approximations for Translational Packing of Convex Polygons
Optimal packing of objects in containers is a critical problem in various real-life and industrial applications. This paper investigates the two-dimensional packing of convex polygons without rotations, where only translations are allowed. We study different settings depending on the type of containers used, including minimizing the number of containers or the size of the container based on an objective function.
Building on prior research in the field, we develop polynomial-time algorithms with improved approximation guarantees upon the best-known results by Alt, de Berg and Knauer, as well as Aamand, Abrahamsen, Beretta and Kleist, for problems such as Polygon Area Minimization, Polygon Perimeter Minimization, Polygon Strip Packing, and Polygon Bin Packing. Our approach utilizes a sequence of object transformations that allows sorting by height and orientation, thus enhancing the effectiveness of shelf packing algorithms for polygon packing problems. In addition, we present efficient approximation algorithms for special cases of the Polygon Bin Packing problem, progressing toward solving an open question concerning an ?(1)-approximation algorithm for arbitrary polygons
Corrigendum to: Approximating minimum-area rectangular and convex containers for packing convex polygons
This note corrects an error in the paper “Approximating minimum-area rectangular and convex containers for packing convex polygons”, which appeared in JoCG, Vol. 8(1), pages 1–10
Improved Approximations for Translational Packing of Convex Polygons
Optimal packing of objects in containers is a critical problem in various
real-life and industrial applications. This paper investigates the
two-dimensional packing of convex polygons without rotations, where only
translations are allowed. We study different settings depending on the type of
containers used, including minimizing the number of containers or the size of
the container based on an objective function.
Building on prior research in the field, we develop polynomial-time
algorithms with improved approximation guarantees upon the best-known results
by Alt, de Berg and Knauer, as well as Aamand, Abrahamsen, Beretta and Kleist,
for problems such as Polygon Area Minimization, Polygon Perimeter Minimization,
Polygon Strip Packing, and Polygon Bin Packing. Our approach utilizes a
sequence of object transformations that allows sorting by height and
orientation, thus enhancing the effectiveness of shelf packing algorithms for
polygon packing problems. In addition, we present efficient approximation
algorithms for special cases of the Polygon Bin Packing problem, progressing
toward solving an open question concerning an O(1)-approximation algorithm for
arbitrary polygons.Comment: This is the full version of the same-named paper which will be
presented at ESA 2023 conferenc
Approximating minimum-area rectangular and convex containers for packing convex polygons
We investigate the problem of finding a minimum-area container for the disjoint packing of a set of convex polygons by translations. In particular, we consider axis-parallel rectangles or arbitrary convex sets as containers. For both optimization problems which are NP-hard we develop efficient constant factor approximation algorithms
Approximating minimum-area rectangular and convex containers for packing convex polygons
We investigate the problem of finding a minimum-area container for the disjoint packing of a set of convex polygons by translations. In particular, we consider axis-parallel rectangles or arbitrary convex sets as containers. For both optimization problems which are NP-hard we develop efficient constant factor approximation algorithms
Approximating minimum-area rectangular and convex containers for packing convex polygons
We investigate the problem of finding a minimum-area container for the disjoint packing of a set of convex polygons by translations. In particular, we consider axis-parallel rectangles or arbitrary convex sets as containers. For both optimization problems which are NP-hard we develop efficient constant factor approximation algorithms
Approximating minimum-area rectangular and convex containers for packing convex polygons
We investigate the problem of finding a minimum-area container for the disjoint packing of a set of convex polygons by translations. In particular, we consider axis-parallel rectangles or arbitrary convex sets as containers. For both optimization problems which are NP-hard we develop efficient constant factor approximation algorithms
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum