Improved Approximation Algorithm for Two-Dimensional Bin Packing
نویسندگان
چکیده
We study the two-dimensional bin packing problem with and without rotations. Here we are given a set of two-dimensional rectangular items I and the goal is to pack these into a minimum number of unit square bins. We consider the orthogonal packing case where the edges of the items must be aligned parallel to the edges of the bin. Our main result is a 1.405approximation for two-dimensional bin packing with and without rotation, which improves upon a recent 1.5 approximation due to Jansen and Prädel. We also show that a wide class of rounding based algorithms cannot improve upon the factor of 1.5.
منابع مشابه
Extending Two-Dimensional Bin Packing Problem: Consideration of Priority for Items
In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...
متن کاملImproved Absolute Approximation Ratios for Two-Dimensional Packing Problems
We consider the two-dimensional bin packing and strip packing problem, where a list of rectangles has to be packed into a minimal number of rectangular bins or a strip of minimal height, respectively. All packings have to be non-overlapping and orthogonal, i.e., axisparallel. Our algorithm for strip packing has an absolute approximation ratio of 1.9396 and is the first algorithm to break the ap...
متن کاملA Three-dimensional Bin Packing Algorithm
In this paper an approximation algorithm for the three-dimensional bin packing problem is proposed and its performance bound is investigated. To obtain such a bound a modified bin packing algorithm is considered for a two-dimensional problem with bounded bin and its area utilization is estimated. Finally, a hard example gives a lower bound of the performance bound. '
متن کاملApproximation algorithms for orthogonal packing problems for hypercubes
Orthogonal packing problems are natural multidimensional generalizations of the classical bin packing problem and knapsack problem and occur in many different settings. The input consists of a set I = {r1, . . . , rn} of d-dimensional rectangular items ri = (ai,1, . . . , ai,d) and a space Q. The task is to pack the items in an orthogonal and non-overlapping manner without using rotations into ...
متن کاملA Heuristic for Improved Genetic Bin Packing
The bin packing optimization problem packs a set of objects into a set of bins so that the amount of wasted space is minimized The bin packing problem has many important applications These include multiprocessor scheduling resource allocation and real world planning packing routing and scheduling optimization problems The bin packing problem is NP complete Since there is therefore little hope i...
متن کامل