Rolf Harren

Packing Rectangles into 2 OPT Bins Using Rotations

Invited Lectures.- A Survey of Results for Deletion Channels and Related Synchronization Channels.- Nash Bargaining Via Flexible Budget Markets.- Contributed Papers.- Simplified Planar Coresets for Data Streams.- Uniquely Represented Data Structures for Computational Geometry.- I/O Efficient Dynamic Data Structures for Longest Prefix Queries.- Guarding Art Galleries: The Extra Cost for Sculptures Is Linear.- Vision-Based Pursuit-Evasion in a Grid.- Angle Optimization in Target Tracking.- Improved Bounds for Wireless Localization.- Bicriteria Approximation Tradeoff for the Node-Cost Budget Problem.- Integer Maximum Flow in Wireless Sensor Networks with Energy Constraint.- The Maximum Energy-Constrained Dynamic Flow Problem.- Bounded Unpopularity Matchings.- Data Structures with Local Update Operations.- On the Redundancy of Succinct Data Structures.- Confluently Persistent Tries for Efficient Version Control.- A Uniform Approach Towards Succinct Representation of Trees.- An Algorithm for L(2,1)-Labeling of Trees.- Batch Coloring Flat Graphs and Thin.- Approximating the Interval Constrained Coloring Problem.- A Path Cover Technique for LCAs in Dags.- Boundary Labeling with Octilinear Leaders.- Distributed Disaster Disclosure.- Reoptimization of Steiner Trees.- On the Locality of Extracting a 2-Manifold in .- On Metric Clustering to Minimize the Sum of Radii.- On Covering Problems of Rado.- Packing Rectangles into 2OPT Bins Using Rotations.- A Preemptive Algorithm for Maximizing Disjoint Paths on Trees.- Minimum Distortion Embeddings into a Path of Bipartite Permutation and Threshold Graphs.- On a Special Co-cycle Basis of Graphs.- A Simple Linear Time Algorithm for the Isomorphism Problem on Proper Circular-Arc Graphs.- Spanners of Additively Weighted Point Sets.- The Kinetic Facility Location Problem.- Computing the Greedy Spanner in Near-Quadratic Time.- Parameterized Computational Complexity of Dodgson and Young Elections.- Online Compression Caching.- On Trade-Offs in External-Memory Diameter-Approximation.We consider the problem of packing rectangles into bins that are unit squares, where the goal is to minimize the number of bins used. All rectangles can be rotated by 90 degrees and have to be packed non- overlapping and orthogonal, i.e., axis-parallel. We present an algorithm for this problem with an absolute worst-case ratio of 2, which is optimal providedP 6NP.

A (5/3+ε )-approximation for strip packing

We study strip packing, which is one of the most classical two-dimensional packing problems: given a collection of rectangles, the problem is to find a feasible orthogonal packing without rotations into a strip of width 1 and minimum height. In this paper we present an approximation algorithm for the strip packing problem with absolute approximation ratio of 5/3+@e for any @e>0. This result significantly narrows the gap between the best known upper bound and the lower bound of 3/2; previously, the best upper bound was 1.9396 due to Harren and van Stee.

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., axis-parallel. Our algorithm for strip packing has an absolute approximation ratio of 1.9396 and is the first algorithm to break the approximation ratio of 2 which was established more than a decade ago. Moreover, we present a polynomial time approximation scheme (

Absolute approximation ratios for packing rectangles into bins

\mathcal{PTAS}

Improved Lower Bound for Online Strip Packing

) for strip packing where rotations by 90 degrees are permitted and an algorithm for two-dimensional bin packing with an absolute worst-case ratio of 2, which is optimal provided

Approximation algorithms for orthogonal packing problems for hypercubes

\mathcal{P} \not= \mathcal{NP}

Approximation Algorithms for 3D Orthogonal Knapsack

.

A (5/3 + ε)-approximation for strip packing

AbstractWe consider the problem of packing rectangles into bins that are unit squares, where the goal is to minimize the number of bins used. All rectangles have to be packed non-overlapping and orthogonal, i.e., axis-parallel. We present an algorithm with an absolute worst-case ratio of 2 for the case where the rectangles can be rotated by 90 degrees. This is optimal provided

Improved lower bound for online strip packing

\mathcal{P}\not=\mathcal{NP}

Packing Rectangles into 2OPT Bins Using Rotations

. For the case where rotation is not allowed, we prove an approximation ratio of 3 for the algorithm Hybrid First Fit which was introduced by Chung et al. (SIAM J. Algebr. Discrete Methods 3(1):66–76, 1982) and whose running time is slightly better than the running time of Zhang’s previously known 3-approximation algorithm (Zhang in Oper. Res. Lett. 33(2):121–126, 2005).