Indexed by:期刊论文

Date of Publication:2013-01-01

Journal:SIAM JOURNAL ON COMPUTING

Included Journals:SCIE、EI、Scopus

Volume:42

Issue:2

Page Number:579-592

ISSN No.:0097-5397

Key Words:strip packing; bin packing; harmonic algorithm

Abstract:In the three-dimensional (3D) strip packing problem, we are given a set of 3D rectangular items and a 3D box B. The goal is to pack all the items in B such that the height of the packing is minimized. We consider the most basic version of the problem, where the items must be packed with their edges parallel to the edges of B and cannot be rotated. Building upon Caprara's work for the two-dimensional (2D) bin packing problem, we obtain an algorithm that, given any epsilon > 0, achieves an approximation of T-infinity + epsilon approximate to 1.69103 + epsilon, where T-infinity is the well-known number that occurs naturally in the context of bin packing. Our key idea is to establish a connection between bin packing solutions for an arbitrary instance I and the strip packing solutions for the corresponding instance obtained from I by applying the harmonic transformation to certain dimensions. Based on this connection, we also give a simple alternate proof of the T-infinity + epsilon approximation for 2D bin packing due to Caprara. In particular, we show how his result follows from a simple modification of the asymptotic approximation scheme for 2D strip packing due to Kenyon and Remila.