@inproceedings{6ed4469c996745d4811cfe458cc51de2,
title = "(Re)packing Equal Disks into Rectangle",
abstract = "The problem of packing of equal disks (or circles) into a rectangle is a fundamental geometric problem. (By a packing here we mean an arrangement of disks in a rectangle without overlapping.) We consider the following algorithmic generalization of the equal disk packing problem. In this problem, for a given packing of equal disks into a rectangle, the question is whether by changing positions of a small number of disks, we can allocate space for packing more disks. More formally, in the repacking problem, for a given set of n equal disks packed into a rectangle and integers k and h, we ask whether it is possible by changing positions of at most h disks to pack n + k disks. Thus the problem of packing equal disks is the special case of our problem with n = h = 0. While the computational complexity of packing equal disks into a rectangle remains open, we prove that the repacking problem is NP-hard already for h = 0. Our main algorithmic contribution is an algorithm that solves the repacking problem in time (h + k)O(h+k) · |I|O(1), where |I| is the input size. That is, the problem is fixed-parameter tractable parameterized by k and h.",
keywords = "circle packing, fixed-parameter tractability, parameterized complexity, unit disks",
author = "Fomin, {Fedor V.} and Golovach, {Petr A.} and Tanmay Inamdar and Meirav Zehavi",
note = "Funding Information: Funding Fedor V. Fomin: Supported by the Research Council of Norway via the project BWCA, grant no. 314528. Petr A. Golovach: Supported by the Research Council of Norway via the project BWCA, grant no. 314528. Tanmay Inamdar: Supported by the European Research Council (ERC) via grant LOPPRE, reference 819416. Meirav Zehavi: Supported by the Israel Science Foundation (ISF) grant no. 1176/18. Publisher Copyright: {\textcopyright} Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, and Meirav Zehavi; licensed under Creative Commons License CC-BY 4.0; 49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022 ; Conference date: 04-07-2022 Through 08-07-2022",
year = "2022",
month = jun,
day = "28",
doi = "10.4230/LIPIcs.ICALP.2022.60",
language = "English",
isbn = "978-3-95977-235-8",
volume = "229",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "60:1--60:17",
editor = "Mikolaj Bojanczyk and Emanuela Merelli and Woodruff, {David P.}",
booktitle = "49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022",
address = "Germany",
}