DeepAI

# Tight Approximation Algorithms for Two Dimensional Guillotine Strip Packing

In the Strip Packing problem (SP), we are given a vertical half-strip [0,W]×[0,∞) and a set of n axis-aligned rectangles of width at most W. The goal is to find a non-overlapping packing of all rectangles into the strip such that the height of the packing is minimized. A well-studied and frequently used practical constraint is to allow only those packings that are guillotine separable, i.e., every rectangle in the packing can be obtained by recursively applying a sequence of edge-to-edge axis-parallel cuts (guillotine cuts) that do not intersect any item of the solution. In this paper, we study approximation algorithms for the Guillotine Strip Packing problem (GSP), i.e., the Strip Packing problem where we require additionally that the packing needs to be guillotine separable. This problem generalizes the classical Bin Packing problem and also makespan minimization on identical machines, and thus it is already strongly NP-hard. Moreover, due to a reduction from the Partition problem, it is NP-hard to obtain a polynomial-time (3/2-ε)-approximation algorithm for GSP for any ε>0 (exactly as Strip Packing). We provide a matching polynomial time (3/2+ε)-approximation algorithm for GSP. Furthermore, we present a pseudo-polynomial time (1+ε)-approximation algorithm for GSP. This is surprising as it is NP-hard to obtain a (5/4-ε)-approximation algorithm for (general) Strip Packing in pseudo-polynomial time. Thus, our results essentially settle the approximability of GSP for both the polynomial and the pseudo-polynomial settings.

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01/23/2018

### Improved Pseudo-Polynomial-Time Approximation for Strip Packing

We study the strip packing problem, a classical packing problem which ge...
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We consider planar tiling and packing problems with polyomino pieces and...
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### Approximation Algorithms for Demand Strip Packing

In the Demand Strip Packing problem (DSP), we are given a time interval ...
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### Packing Rotating Segments

We show that the following variant of labeling rotating maps is NP-hard,...
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### Closing the gap for pseudo-polynomial strip packing

We study pseudo-polynomial Strip Packing. Given a set of rectangular axi...
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### Approximation Algorithms for ROUND-UFP and ROUND-SAP

We study ROUND-UFP and ROUND-SAP, two generalizations of the classical B...
05/15/2021

### Peak Demand Minimization via Sliced Strip Packing

We study Nonpreemptive Peak Demand Minimization (NPDM) problem, where we...