Lars Prädel

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.

Two for One: Tight Approximation of 2D Bin Packing

In this paper, we study the two-dimensional geometrical bin packing problem (2DBP): given a list of rectangles, provide a packing of all these into the smallest possible number of 1×1 bins without rotating the rectangles. We present a 2-approximate algorithm, which improves over the previous best known ratio of 3, matches the best results for the rotational case and also matches the known lower bound of approximability. Our approach makes strong use of a recently-discovered PTAS for a related knapsack problem and a new algorithm that can pack instances into OPT + 2 bins for any constant OPT.

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 approximation ratio of 5/3 + e for any e > 0. This result significantly narrows the gap between the best known upper bounds of 2 by Schiermeyer and Steinberg and 1.9396 by Harren and van Stee and the lower bound of 3/2.

A New Asymptotic Approximation Algorithm for 3-Dimensional Strip Packing

We study the 3-dimensional Strip Packing problem: Given a list of n boxes b 1,…,b n of the width w i ≤ 1, depth d i ≤ 1 and an arbitrary length l i . The objective is to pack all boxes into a strip of the width and depth 1 and infinite length, so that the packing length is minimized. The boxes may not overlap or be rotated. We present an improvement of the current best asymptotic approximation ratio of 1.692 by Bansal et al.[2] with an asymptotic 3/2 + e-approximation for any e > 0.

TWO FOR ONE: TIGHT APPROXIMATION OF 2D BIN PACKING

In this paper, we study the two-dimensional geometrical bin packing problem (2DBP): given a list of rectangles, provide a packing of all these into the smallest possible number of unit bins without rotating the rectangles. Beyond its theoretical appeal, this problem has many practical applications, for example in print layout and VLSI chip design. We present a 2-approximate algorithm, which improves over the previous best known ratio of 3, matches the best results for the problem where rotations are allowed and also matches the known lower bound of approximability. Our approach makes strong use of a PTAS for a related 2D knapsack problem and a new algorithm that can pack instances into two bins if OPT = 1.

Tight approximation algorithms for scheduling with fixed jobs and nonavailability

We study two closely related problems in nonpreemptive scheduling of jobs on identical parallel machines. In these two settings there are either fixed jobs or nonavailability intervals during which the machines are not available; in both cases, the objective is to minimize the makespan. Both formulations have different applications, for example, in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of 3/2. For scheduling with fixed jobs, a lower bound of 3/2 on the approximation ratio has been obtained by Scharbrodt et al. [1999]; for scheduling with nonavailability we provide the same lower bound. We use dual approximation, creation of a gap structure, and a PTAS for the multiple subset sum problem, combined with a postprocessing step to assign large jobs.

A -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.

A (5/3+ε)(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.