
Improved PseudoPolynomialTime Approximation for Strip Packing
We study the strip packing problem, a classical packing problem which ge...
read it

Optimal Rectangle Packing: An Absolute Placement Approach
We consider the problem of finding all enclosing rectangles of minimum a...
read it

Enumerating All Convex Polyhedra Glued from Squares in Polynomial Time
We present an algorithm that enumerates and classifies all edgetoedge ...
read it

A study on loadbalanced variants of the bin packing problem
We consider several extensions of the fractional bin packing problem, a ...
read it

Framework for ∃ℝCompleteness of TwoDimensional Packing Problems
We show that many natural twodimensional packing problems are algorithm...
read it

Rectangle Blanket Problem: Binary integer linear programming formulation and solution algorithms
A rectangle blanket is a set of nonoverlapping axisaligned rectangles,...
read it

Tromino Tilings with Pegs via Flow Networks
A tromino tiling problem is a packing puzzle where we are given a region...
read it
Tiling with Squares and Packing Dominos in Polynomial Time
We consider planar tiling and packing problems with polyomino pieces and a polyomino container P. A polyomino is a polygonal region with axis parallel edges and corners of integral coordinates, which may have holes. We give two polynomial time algorithms, one for deciding if P can be tiled with 2× 2 squares (that is, deciding if P is the union of a set of nonoverlapping copies of the 2× 2 square) and one for packing P with a maximum number of nonoverlapping and axisparallel 2× 1 dominos, allowing rotations of 90^∘. As packing is more general than tiling, the latter algorithm can also be used to decide if P can be tiled by 2× 1 dominos. These are classical problems with important applications in VLSI design, and the related problem of finding a maximum packing of 2× 2 squares is known to be NPHard [J. Algorithms 1990]. For our three problems there are known pseudopolynomial time algorithms, that is, algorithms with running times polynomial in the area of P. However, the standard, compact way to represent a polygon is by listing the coordinates of the corners in binary. We use this representation, and thus present the first polynomial time algorithms for the problems. Concretely, we give a simple O(nlog n) algorithm for tiling with squares, and a more involved O(n^4) algorithm for packing and tiling with dominos.
READ FULL TEXT
Comments
There are no comments yet.