Invited Paper: Distributed Rhombus Formation of Sliding Squares Kostitsyna, Irina Liedtke, David Jan Scheideler, Christian Bonomi, Silvia Mandal, Partha Sarathi Robinson, Peter Sharma, Gokarna Tixeuil, Sebastien 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. Springer Nature Switzerland 2025 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://ris.uni-paderborn.de/record/62285 Kostitsyna I, Liedtke DJ, Scheideler C. Invited Paper: Distributed Rhombus Formation of Sliding Squares. In: Bonomi S, Mandal PS, Robinson P, Sharma G, Tixeuil S, eds. <i>Stabilization, Safety, and Security of Distributed Systems</i>. Springer Nature Switzerland; 2025:325-342. doi:<a href="https://doi.org/10.1007/978-3-032-11127-2_26">10.1007/978-3-032-11127-2_26</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-032-11127-2_26 info:eu-repo/semantics/altIdentifier/issn/0302-9743 info:eu-repo/semantics/altIdentifier/issn/1611-3349 info:eu-repo/semantics/altIdentifier/isbn/9783032111265 info:eu-repo/semantics/altIdentifier/isbn/9783032111272 info:eu-repo/semantics/closedAccess