Rob van Stee

Speed Scaling of Tasks with Precedence Constraints

Abstract We consider the problem of speed scaling to conserve energy in a multiprocessor setting where there are precedence constraints between tasks, and where the performance measure is the makespan. That is, we consider an energy bounded version of the classic problem Pm|prec|Cmax . We extend the standard 3-field notation and denote this problem as Sm|prec, energy|Cmax . We show that, without loss of generality, one need only consider constant power schedules. We then show how to reduce this problem to the problem Qm|prec|Cmax  to obtain a poly-log(m)-approximation algorithm.

On strip packing With rotations

We present an asymptotic fully polynomial time approximation scheme for two-dimensional strip packing with rotations. In this problem, a set of rectangles need to be packed into a rectangle (strip) of fixed width and minimum height, and these rectangles can be rotated by 90°. Additionally, we present a simple asymptotic polynomial time approximation scheme, and give an improved algorithm for two-dimensional bin packing with rotations.

New Bounds for Variable-Sized Online Bin Packing

In the variable-sized online bin packing problem, one has to assign items to bins one by one. The bins are drawn from some fixed set of sizes, and the goal is to minimize the sum of the sizes of the bins used. We present new algorithms for this problem and show upper bounds for them which improve on the best previous upper bounds. We also show the first general lower bounds for this problem. The case in which bins of two sizes, 1 and

Online square and cube packing

\alpha \in (0,1)

Packing Rectangles into 2 OPT Bins Using Rotations

, are used is studied in detail. This investigation leads us to the discovery of several interesting fractal-like curves.

Optimal Online Algorithms for Multidimensional Packing Problems

In online square packing, squares of different sizes arrive online and need to be packed into unit squares which are called bins. The goal is to minimize the number of bins used. Online cube packing is defined analogously. We show an upper bound of 2.2697 and a lower bound of 1.6406 for online square packing, and an upper bound of 2.9421 and a lower bound of 1.6680 for online cube packing. The upper bound for squares can be further reduced to 2.24437 using a computer proof. These results improve on the previously known results for the two problems. We also show improved lower bounds for higher dimensions.

On the price of stability for undirected network design

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.

Preemptive scheduling in overloaded systems

We solve an open problem in the literature by providing an online algorithm for multidimensional bin packing that uses only bounded space. To achieve this, we introduce a new technique for classifying the items to be packed. We show that our algorithm is optimal among bounded space algorithms for any dimension

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

d>1

Improved Absolute Approximation Ratios for Two-Dimensional Packing Problems

. Its asymptotic performance ratio is