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Polynomiality for Bin Packing with a Constant Number of Item Types
Name
1307.5108.pdf
Size
274.63 KB
Format
Adobe PDF
Checksum (MD5)
f5c7e8e8c0e8596e270d2eb10ba5519f
Author(s)
Goemans, Michel X
Rothvoss, Thomas
Date Issued
2020
Journal
Journal of the ACM
Publisher
Association for Computing Machinery (ACM)
Version
Original manuscript
Abstract
© 2020 ACM. We consider the bin packing problem with d different item sizes si and item multiplicities ai, where all numbers are given in binary encoding. This problem formulation is also known as the one-dimensional cutting stock problem. In this work, we provide an algorithm that, for constant d, solves bin packing in polynomial time. This was an open problem for all d ≥ 3. In fact, for constant d our algorithm solves the following problem in polynomial time: Given two d-dimensional polytopes P and Q, find the smallest number of integer points in P whose sum lies in Q. Our approach also applies to high multiplicity scheduling problems in which the number of copies of each job type is given in binary encoding and each type comes with certain parameters such as release dates, processing times, and deadlines. We show that a variety of high multiplicity scheduling problems can be solved in polynomial time if the number of job types is constant.
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Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
10.1145/3421750
