An Approximation Scheme for Strip Packing of Rectangles with Bounded Dimensions
نویسندگان
چکیده
It is shown that for any positive E the strip-packing problem, i.e. the problem of packing a given list of rectangles into a strip of width 1 and minimum height. can be solled within I c 2: times the optimal height, in linear time, if the heights and widths of these rectangles are all bounded below by an absolute constant 2 >O. @ 1998 Elsevicr Science B.V. All rights reserved. K~YIYJY~/S: Strip packing; Approximation algorithms
منابع مشابه
A new metaheuristic genetic-based placement algorithm for 2D strip packing
Given a container of fixed width, infinite height and a set of rectangular block, the 2D-strip packing problem consists of orthogonally placing all the rectangles such that the height is minimized. The position is subject to confinement of no overlapping of blocks. The problem is a complex NP-hard combinatorial optimization, thus a heuristic based on genetic algorithm is proposed to solve it. I...
متن کاملA Structural Lemma in 2-Dimensional Packing, and Its Implications on Approximability
We present a new lemma stating that, given an arbitrary packing of a set of rectangles into a larger rectangle, a “structured” packing of nearly the same set of rectangles exists. This lemma has several implications on the approximability of 2-dimensional packing problems. In this paper, we use it to show the existence of a polynomial-time approximation scheme for 2-dimensional geometric knapsa...
متن کاملImproved Pseudo-Polynomial-Time Approximation for Strip Packing
We study the strip packing problem, a classical packing problem which generalizes both bin packing and makespan minimization. Here we are given a set of axis-parallel rectangles in the two-dimensional plane and the goal is to pack them in a vertical strip of fixed width such that the height of the obtained packing is minimized. The packing must be non-overlapping and the rectangles cannot be ro...
متن کاملA THEORETICALLY CORRECT RESOURCE USAGE VISUALIZATION FOR THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM
The cumulative resource constraints of the resource-constrained project scheduling problem (RCPSP) do not treat the resource demands as geometric rectangles, that is, activities are not necessarily assigned to the same resource units over their processing times. In spite of this fact, most papers on resource-constrained project scheduling mainly in the motivation phase use a strip packing of re...
متن کاملStrip Packing with Slicing
In the strip packing problem, a given set of axis-aligned rectangles must be packed into a fixed-width strip, and the goal is to minimize the height of the strip. In this paper, we examine a variant in which each rectangle may be cut vertically into multiple slices and the slices may be packed into the strip as individual pieces. Our results are: (1) analysis of the approximation ratio of sever...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 82 شماره
صفحات -
تاریخ انتشار 1998