[{"year":"2025","title":"Invited Paper: Distributed Rhombus Formation of Sliding Squares","publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783032111265","9783032111272"]},"author":[{"full_name":"Kostitsyna, Irina","first_name":"Irina","last_name":"Kostitsyna"},{"id":"55557","last_name":"Liedtke","first_name":"David Jan","full_name":"Liedtke, David Jan"},{"first_name":"Christian","last_name":"Scheideler","full_name":"Scheideler, Christian","id":"20792"}],"date_updated":"2026-02-11T08:31:14Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1007/978-3-032-11127-2_26","publication":"Stabilization, Safety, and Security of Distributed Systems","abstract":[{"lang":"eng","text":"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."}],"date_created":"2025-11-23T21:07:12Z","type":"conference","department":[{"_id":"79"}],"status":"public","conference":{"end_date":"2025-10-11","location":"Kathmandu","name":"27th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)","start_date":"2025-10-09"},"page":"325-342","_id":"62285","publisher":"Springer Nature Switzerland","user_id":"15578","editor":[{"first_name":"Silvia","last_name":"Bonomi","full_name":"Bonomi, Silvia"},{"last_name":"Mandal","first_name":"Partha Sarathi","full_name":"Mandal, Partha Sarathi"},{"full_name":"Robinson, Peter","last_name":"Robinson","first_name":"Peter"},{"first_name":"Gokarna","last_name":"Sharma","full_name":"Sharma, Gokarna"},{"first_name":"Sebastien","last_name":"Tixeuil","full_name":"Tixeuil, Sebastien"}],"citation":{"apa":"Kostitsyna, I., Liedtke, D. J., &#38; Scheideler, C. (2025). Invited Paper: Distributed Rhombus Formation of Sliding Squares. In S. Bonomi, P. S. Mandal, P. Robinson, G. Sharma, &#38; S. Tixeuil (Eds.), <i>Stabilization, Safety, and Security of Distributed Systems</i> (pp. 325–342). Springer Nature Switzerland. <a href=\"https://doi.org/10.1007/978-3-032-11127-2_26\">https://doi.org/10.1007/978-3-032-11127-2_26</a>","ieee":"I. Kostitsyna, D. J. Liedtke, and C. Scheideler, “Invited Paper: Distributed Rhombus Formation of Sliding Squares,” in <i>Stabilization, Safety, and Security of Distributed Systems</i>, Kathmandu, 2025, pp. 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>.","short":"I. Kostitsyna, D.J. Liedtke, C. Scheideler, in: S. Bonomi, P.S. Mandal, P. Robinson, G. Sharma, S. Tixeuil (Eds.), Stabilization, Safety, and Security of Distributed Systems, Springer Nature Switzerland, Cham, 2025, pp. 325–342.","chicago":"Kostitsyna, Irina, David Jan Liedtke, and Christian Scheideler. “Invited Paper: Distributed Rhombus Formation of Sliding Squares.” In <i>Stabilization, Safety, and Security of Distributed Systems</i>, edited by Silvia Bonomi, Partha Sarathi Mandal, Peter Robinson, Gokarna Sharma, and Sebastien Tixeuil, 325–42. Cham: Springer Nature Switzerland, 2025. <a href=\"https://doi.org/10.1007/978-3-032-11127-2_26\">https://doi.org/10.1007/978-3-032-11127-2_26</a>.","mla":"Kostitsyna, Irina, et al. “Invited Paper: Distributed Rhombus Formation of Sliding Squares.” <i>Stabilization, Safety, and Security of Distributed Systems</i>, edited by Silvia Bonomi et al., Springer Nature Switzerland, 2025, pp. 325–42, doi:<a href=\"https://doi.org/10.1007/978-3-032-11127-2_26\">10.1007/978-3-032-11127-2_26</a>.","ama":"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>","bibtex":"@inproceedings{Kostitsyna_Liedtke_Scheideler_2025, place={Cham}, title={Invited Paper: Distributed Rhombus Formation of Sliding Squares}, DOI={<a href=\"https://doi.org/10.1007/978-3-032-11127-2_26\">10.1007/978-3-032-11127-2_26</a>}, booktitle={Stabilization, Safety, and Security of Distributed Systems}, publisher={Springer Nature Switzerland}, author={Kostitsyna, Irina and Liedtke, David Jan and Scheideler, Christian}, editor={Bonomi, Silvia and Mandal, Partha Sarathi and Robinson, Peter and Sharma, Gokarna and Tixeuil, Sebastien}, year={2025}, pages={325–342} }"},"place":"Cham"}]