Two packing problems

Improved 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...

Algorithms for Two-Dimensional Bin Packing and Assignment Problems

Invited Review Two-dimensional packing problems: A survey

We consider problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste. In two-dimensional bin packing problems these units are finite rectangles, and the objective is to pack all the items into the minimum number of units, while in two-dimensional strip packing problems there is a single standardized unit of given width, and the o...

Approximation algorithms for scheduling and two-dimensional packing problems

This dissertation thesis is concerned with two topics of combinatorial optimization: scheduling and geometrical packing problems. Scheduling deals with the assignment of jobs to machines in a ‘good’ way, for suitable notions of good. Two particular problems are studied in depth: on the one hand, we consider the impact of machine failure on online scheduling, i.e. what are the consequences of th...

Recent advances on two-dimensional bin packing problems

We survey recent advances obtained for the two-dimensional bin packing problem, with special emphasis on exact algorithms and e1ective heuristic and metaheuristic approaches. ? 2002 Elsevier Science B.V. All rights reserved.