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High multiplicity N-fold IP via configuration LP
Citation Link: https://doi.org/10.15480/882.4606
Publikationstyp
Journal Article
Date Issued
2023-06
Sprache
English
Institut
TORE-DOI
Journal
Volume
200
Issue
1
Start Page
199
End Page
227
Citation
Mathematical Programming (2023)
Publisher DOI
Scopus ID
Publisher
Springer
Peer Reviewed
true
N-fold integer programs (IPs) form an important class of block-structured IPs for which increasingly fast algorithms have recently been developed and successfully applied. We study high-multiplicity N-fold IPs, which encode IPs succinctly by presenting a description of each block type and a vector of block multiplicities. Our goal is to design algorithms which solve N-fold IPs in time polynomial in the size of the succinct encoding, which may be significantly smaller than the size of the explicit (non-succinct) instance. We present the first fixed-parameter algorithm for high-multiplicity N-fold IPs, which even works for convex objectives. Our key contribution is a novel proximity theorem which relates fractional and integer optima of the Configuration LP, a fundamental notion by Gilmore and Gomory [Oper. Res., 1961] which we generalize. Our algorithm for N-fold IP is faster than previous algorithms whenever the number of blocks is much larger than the number of block types, such as in N-fold IP models for various scheduling problems.
Subjects
Integer programming
Configuration IP
Fixed-parameter algorithms
Scheduling
DDC Class
510: Mathematik
Publication version
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