Tile-Packing Tomography Is $\mathbb{NP}$ -hard
نویسندگان
چکیده
منابع مشابه
Tile Packing Tomography is NP-hard
Discrete tomography deals with reconstructing finite spatial objects from their projections. The objects we study in this paper are called tilings or tile-packings, and they consist of a number of disjoint copies of a fixed tile, where a tile is defined as a connected set of grid points. A row projection specifies how many grid points are covered by tiles in a given row; column projections are ...
متن کاملThe Tile Packing Problem
The tile packing problem is a challenging combinatorial puzzle based on tiles with colored edges or colored corners. In its different incarnations, the puzzle gives rise to a number of interesting problems. In this paper, we sketch the background of the tile packing problem and present solutions to the puzzle. We hope that this work will stimulate further interest in this puzzle amongst readers...
متن کاملPacking identical simple polygons is NP-hard
Given a small polygon S, a big simple polygon B and a positive integer k, it is shown to be NP-hard to determine whether k copies of the small polygon (allowing translation and rotation) can be placed in the big polygon without overlap. Previous NP-hardness results were only known in the case where the big polygon is allowed to be non-simple. A novel reduction from Planar-Circuit-SAT is present...
متن کاملCircle Packing for Origami Design Is Hard
Over the last 20 years, the world of origami has been changed by the introduction of design algorithms that bear a close relationship to, if not outright ancestry from, computational geometry. One of the first robust algorithms for origami design was the circle/river method (also called the tree method) developed independently by Lang [7–9] and Meguro [12, 13]. This algorithm and its variants p...
متن کاملPacking Segments in a Convex 3-Polytope is NP-hard
We show it is NP-hard to pack the maximum number of segments in a convex 3-dimensional polytope. We show this packing problem is also NP-hard for general polygonal regions in the plane. This problem relates two streams of research, Kakeya set problems and packing problems.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algorithmica
سال: 2011
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-011-9498-1