Two-dimensional packing problems in telecommunications

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...

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...

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...

Algorithms for Two-Dimensional Bin Packing and Assignment Problems

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.