@inproceedings{458a1f62c0d24295aba0205e9604b751,
title = "Tight Lower Bounds for Block-Structured Integer Programs",
abstract = "We study fundamental block-structured integer programs called tree-fold and multi-stage IPs. Tree-fold IPs admit a constraint matrix with independent blocks linked together by few constraints in a recursive pattern; and transposing their constraint matrix yields multi-stage IPs. The state-of-the-art algorithms to solve these IPs have an exponential gap in their running times, making it natural to ask whether this gap is inherent. We answer this question affirmative. Assuming the Exponential Time Hypothesis, we prove lower bounds showing that the exponential difference is necessary, and that the known algorithms are near optimal. Moreover, we prove unconditional lower bounds on the norms of the Graver basis, a fundamental building block of all known algorithms to solve these IPs. This shows that none of the current approaches can be improved beyond this bound.",
keywords = "(unconditional) lower bounds, ETH, integer programming, multi-stage, n-fold, subset sum, tree-fold",
author = "Christoph Hunkenschr{\"o}der and Kim-Manuel Klein and Martin Kouteck{\'y} and Alexandra Lassota and Asaf Levin",
year = "2024",
month = may,
day = "22",
doi = "10.1007/978-3-031-59835-7\_17",
language = "English",
isbn = "978-3-031-59834-0",
series = "Lecture Notes in Computer Science (LNCS)",
publisher = "Springer",
pages = "224--237",
editor = "Jens Vygen and Jaros{\l}aw Byrka",
booktitle = "Integer Programming and Combinatorial Optimization",
address = "Germany",
note = "25th Conference on Integer Programming and Combinatorial Optimization, IPCO 2024, IPCO 2024 ; Conference date: 03-07-2024 Through 05-07-2024",
}