Distributed rhombus formation of sliding squares Kostitsyna, Irina Liedtke, David Scheideler, Christian modular robots distributed algorithms sliding squares The sliding square model is a widely used abstraction for studying self-reconfigurable robotic systems, where modules are square-shaped robots that move by sliding or rotating over one another. In this paper, we propose a novel distributed algorithm that enables a group of modules to reconfigure into a rhombus shape, starting from an arbitrary side-connected configuration. It is connectivity-preserving and operates under minimal assumptions: one leader module, common chirality, constant memory per module, and visibility and communication restricted to immediate neighbors. Unlike prior work, which relaxes the original sliding square move-set, our approach uses the unmodified move-set, addressing the additional challenge of handling locked configurations. Our algorithm is sequential in nature and operates with a worst-case time complexity of O(n^2) rounds, which is optimal for sequential algorithms. To improve runtime, we introduce two parallel variants of the algorithm. Both rely on a spanning tree data structure, allowing modules to make decisions based on local connectivity. Our experimental results show a significant speedup for the first variant, and a linear average runtime for the second variant, which is worst-case optimal for parallel algorithms. Elsevier BV 2026 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://ris.uni-paderborn.de/record/66838 Kostitsyna I, Liedtke D, Scheideler C. Distributed rhombus formation of sliding squares. <i>Theoretical Computer Science</i>. 2026;1085. doi:<a href="https://doi.org/10.1016/j.tcs.2026.116196">10.1016/j.tcs.2026.116196</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2026.116196 info:eu-repo/semantics/altIdentifier/issn/0304-3975 info:eu-repo/semantics/closedAccess