@inproceedings{7816e530ebee411aa1ba77cfb78e55d6,
title = "Approximating Red-Blue Set Cover and Minimum Monotone Satisfying Assignment",
abstract = "We provide new approximation algorithms for the Red-Blue Set Cover and Circuit Minimum Monotone Satisfying Assignment (MMSA) problems. Our algorithm for Red-Blue Set Cover achieves {\~O}(m1/3)-approximation improving on the {\~O}(m1/2)-approximation due to Elkin and Peleg (where m is the number of sets). Our approximation algorithm for MMSAt (for circuits of depth t) gives an {\~O}(N1−δ) approximation for δ = 1323−⌈t/2⌉, where N is the number of gates and variables. No non-trivial approximation algorithms for MMSAt with t ≥ 4 were previously known. We complement these results with lower bounds for these problems: For Red-Blue Set Cover, we provide a nearly approximation preserving reduction from Min k-Union that gives an {\~Ω}(m1/4−ε) hardness under the Dense-vs-Random conjecture, while for MMSA we sketch a proof that an SDP relaxation strengthened by Sherali–Adams has an integrality gap of N1−ε where ε → 0 as the circuit depth t → ∞.",
keywords = "Circuit Minimum Monotone Satisfying Assignment (MMSA) Problem, LP Rounding, Red-Blue Set Cover Problem",
author = "Eden Chlamt{\'a}{\v c} and Yury Makarychev and Ali Vakilian",
note = "Publisher Copyright: {\textcopyright} 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.; 26th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2023 and the 27th International Conference on Randomization and Computation, RANDOM 2023 ; Conference date: 11-09-2023 Through 13-09-2023",
year = "2023",
month = sep,
day = "1",
doi = "10.4230/LIPIcs.APPROX/RANDOM.2023.11",
language = "American English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Nicole Megow and Adam Smith",
booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2023",
address = "Germany",
}