An instance of the two-dimensional strip packing problem is specified by n rectangular items, each having a width, 0 < wn ≤ 1, and height, 0 < hn ≤ 1. The objective is to place these items into a strip of width 1, without rotations, such that they are nonoverlapping and the total height of the resulting packing is minimized. In this thesis, we consider the version of the twodimensional strip pa...

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...

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 ...

We study the well-known two-dimensional strip packing problem. Given is a set of rectangular axis-parallel items and a strip of width W with infinite height. The objective is to find a packing of these items into the strip, which minimizes the packing height. Lately, it has been shown that the lower bound of 3/2 of the absolute approximation ratio can be beaten when we allow a pseudo-polynomial...

We present a genetic programming hyper-heuristic system to evolve a ‘disposable’ heuristic for each of a wide range of benchmark instances of the two-dimensional strip packing problem. The evolved heuristics are constructive, and decide both which piece to pack next and where to place that piece, given the current partial solution. Usually, there is a trade-off between the generality of a packi...

This paper deals with a particular “packing” problem, namely the two dimensional strip packing problem, where a finite set of objects have to be located in a strip of fixed width and infinite height. The variant studied here considers regular items (they are rectangular to be more precise) that must be packed without overlap, rotations being not allowed. The objective is to minimize the height ...

We study certain adversary sequences for online strip packing which were first designed and investigated by Brown, Baker and Katseff (Acta Inform. 18:207– 225) and determine the optimal competitive ratio for packing such Brown-BakerKatseff sequences online. As a byproduct of our result, we get a new lower bound of ρ ≥ 3/2 +√33/6 ≈ 2.457 for the competitive ratio of online strip packing.

The oriented non-guillotine two-dimensional strip packing problem is investigated. Several 1D relaxations are considered and compared. Moreover, an ILP formulation of the 1D contiguous relaxation is given. The appropriate combination of some of the relaxations enables us the formulate a new ILP model of the strip packing problem.

We study the problem of scheduling independent jobs in a hypercube where jobs are executed in subcubes of various dimensions. The problem being NP-complete, several approximation algorithms based on list scheduling have been proposed, having approximation ratio of order of 2. In this paper, a linear time &-approximation algorithm for the problem is provided when the size of the hypercube is fix...