Knop, DušanDušanKnopKoutecký, MartinMartinKouteckýLevin, AsafAsafLevinMnich, MatthiasMatthiasMnichOnn, ShmuelShmuelOnn2022-08-102022-08-102023-06Mathematical Programming (2023)http://hdl.handle.net/11420/13427N-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.en0025-561020231199227Springerhttps://creativecommons.org/licenses/by/4.0/Integer programmingConfiguration IPFixed-parameter algorithmsSchedulingMathematikJournal Article10.15480/882.460610.1007/s10107-022-01882-910.15480/882.4606Journal Article