2026-09-05T12:01:01Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25902 2026-06-23T13:00:31Z ddc:004 open_access

Sliding Cubes in Parallel (Media Exposition) A. Akitaya, Hugo Dorfer, Joseph Kramer, Peter Rieck, Christian Samanta, Soham Shahrouzi, Gabriel Stock, Frederick Sliding squares parallel motion reconfigurability three dimensions constant makespan log-APX hardness NP-hardness worst-case optimality The sliding cubes model serves as a well-established theoretical framework for formalizing and analyzing reconfiguration algorithms in modular robotic systems built from face-connected cubic modules. We extend the parallel sliding cubes model from two to three dimensions, presenting new algorithms, surprising complexity results, and a generalization of the best known bounds from two to three dimensions. A companion video visualizes and explains our results. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Hugo A. Akitaya and Joseph Dorfer and Peter Kramer and Christian Rieck and Soham Samanta and Gabriel Shahrouzi and Frederick Stock 2026 Is Part Of LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2026.96 urn:nbn:de:0030-drops-259020 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.96 eng https://creativecommons.org/licenses/by/4.0/legalcode