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While recent research has focused on chain topologies where nodes need to be linearized with respect to their identiers, we explore a natural and relevant 2-dimensional generalization. In particular, we present a local self-stabilizing algorithm DStab which is based on the concept of \\local Delaunay graphs\" and which forwards temporary edges in greedy fashion reminiscent of compass routing. DStab constructs a Delaunay graph from any initial connected topology and in a distributed manner in time O(n3) in the worst-case; if the initial network contains the Delaunay graph, the convergence time is only O(n) rounds. DStab also ensures that individual node joins and leaves aect a small part of the network only. Such self-stabilizing Delaunay networks have interesting applications and our construction gives insights into the necessary geometric reasoning that is required for higherdimensional linearization problems.Keywords: Distributed Algorithms, Topology Control, Social Networks"}],"file":[{"file_id":"1272","content_type":"application/pdf","success":1,"relation":"main_file","date_updated":"2018-03-15T10:16:20Z","file_name":"570-Delaunay-Journal.pdf","access_level":"closed","file_size":250051,"date_created":"2018-03-15T10:16:20Z","creator":"florida"}],"date_created":"2017-10-17T12:42:43Z","type":"journal_article","department":[{"_id":"79"}],"title":"Towards higher-dimensional topological self-stabilization: A distributed algorithm for Delaunay graphs","year":"2012","author":[{"full_name":"Jacob, Riko","last_name":"Jacob","first_name":"Riko"},{"full_name":"Ritscher, Stephan","last_name":"Ritscher","first_name":"Stephan"},{"full_name":"Scheideler, Christian","first_name":"Christian","last_name":"Scheideler","id":"20792"},{"full_name":"Schmid, Stefan","first_name":"Stefan","last_name":"Schmid"}],"date_updated":"2022-01-06T07:02:36Z","doi":"10.1016/j.tcs.2012.07.029","file_date_updated":"2018-03-15T10:16:20Z","citation":{"short":"R. Jacob, S. Ritscher, C. Scheideler, S. Schmid, Theoretical Computer Science (2012) 137–148.","chicago":"Jacob, Riko, Stephan Ritscher, Christian Scheideler, and Stefan Schmid. “Towards Higher-Dimensional Topological Self-Stabilization: A Distributed Algorithm for Delaunay Graphs.” <i>Theoretical Computer Science</i>, 2012, 137–48. <a href=\"https://doi.org/10.1016/j.tcs.2012.07.029\">https://doi.org/10.1016/j.tcs.2012.07.029</a>.","ieee":"R. Jacob, S. Ritscher, C. Scheideler, and S. Schmid, “Towards higher-dimensional topological self-stabilization: A distributed algorithm for Delaunay graphs,” <i>Theoretical Computer Science</i>, pp. 137–148, 2012.","apa":"Jacob, R., Ritscher, S., Scheideler, C., &#38; Schmid, S. (2012). Towards higher-dimensional topological self-stabilization: A distributed algorithm for Delaunay graphs. <i>Theoretical Computer Science</i>, 137–148. <a href=\"https://doi.org/10.1016/j.tcs.2012.07.029\">https://doi.org/10.1016/j.tcs.2012.07.029</a>","bibtex":"@article{Jacob_Ritscher_Scheideler_Schmid_2012, title={Towards higher-dimensional topological self-stabilization: A distributed algorithm for Delaunay graphs}, DOI={<a href=\"https://doi.org/10.1016/j.tcs.2012.07.029\">10.1016/j.tcs.2012.07.029</a>}, journal={Theoretical Computer Science}, publisher={Elsevier}, author={Jacob, Riko and Ritscher, Stephan and Scheideler, Christian and Schmid, Stefan}, year={2012}, pages={137–148} }","ama":"Jacob R, Ritscher S, Scheideler C, Schmid S. Towards higher-dimensional topological self-stabilization: A distributed algorithm for Delaunay graphs. <i>Theoretical Computer Science</i>. 2012:137-148. doi:<a href=\"https://doi.org/10.1016/j.tcs.2012.07.029\">10.1016/j.tcs.2012.07.029</a>","mla":"Jacob, Riko, et al. “Towards Higher-Dimensional Topological Self-Stabilization: A Distributed Algorithm for Delaunay Graphs.” <i>Theoretical Computer Science</i>, Elsevier, 2012, pp. 137–48, doi:<a href=\"https://doi.org/10.1016/j.tcs.2012.07.029\">10.1016/j.tcs.2012.07.029</a>."},"project":[{"_id":"1","name":"SFB 901"},{"_id":"5","name":"SFB 901 - Subprojekt A1"},{"name":"SFB 901 - Project Area A","_id":"2"}],"status":"public","has_accepted_license":"1","page":"137-148","_id":"570","publisher":"Elsevier","user_id":"477","ddc":["040"]},{"page":"18-35","_id":"574","publisher":"Elsevier","user_id":"477","ddc":["040"],"status":"public","has_accepted_license":"1","file_date_updated":"2018-03-15T09:09:29Z","citation":{"chicago":"Clouser, Thomas, Mikhail Nesterenko, and Christian Scheideler. “Tiara: A Self-Stabilizing Deterministic Skip List and Skip Graph.” <i>Theoretical Computer Science</i>, 2012, 18–35. <a href=\"https://doi.org/10.1016/j.tcs.2011.12.079\">https://doi.org/10.1016/j.tcs.2011.12.079</a>.","short":"T. Clouser, M. Nesterenko, C. Scheideler, Theoretical Computer Science (2012) 18–35.","ieee":"T. Clouser, M. Nesterenko, and C. Scheideler, “Tiara: A self-stabilizing deterministic skip list and skip graph,” <i>Theoretical Computer Science</i>, pp. 18–35, 2012.","apa":"Clouser, T., Nesterenko, M., &#38; Scheideler, C. (2012). Tiara: A self-stabilizing deterministic skip list and skip graph. <i>Theoretical Computer Science</i>, 18–35. <a href=\"https://doi.org/10.1016/j.tcs.2011.12.079\">https://doi.org/10.1016/j.tcs.2011.12.079</a>","bibtex":"@article{Clouser_Nesterenko_Scheideler_2012, title={Tiara: A self-stabilizing deterministic skip list and skip graph}, DOI={<a href=\"https://doi.org/10.1016/j.tcs.2011.12.079\">10.1016/j.tcs.2011.12.079</a>}, journal={Theoretical Computer Science}, publisher={Elsevier}, author={Clouser, Thomas and Nesterenko, Mikhail and Scheideler, Christian}, year={2012}, pages={18–35} }","ama":"Clouser T, Nesterenko M, Scheideler C. Tiara: A self-stabilizing deterministic skip list and skip graph. <i>Theoretical Computer Science</i>. 2012:18-35. doi:<a href=\"https://doi.org/10.1016/j.tcs.2011.12.079\">10.1016/j.tcs.2011.12.079</a>","mla":"Clouser, Thomas, et al. “Tiara: A Self-Stabilizing Deterministic Skip List and Skip Graph.” <i>Theoretical Computer Science</i>, Elsevier, 2012, pp. 18–35, doi:<a href=\"https://doi.org/10.1016/j.tcs.2011.12.079\">10.1016/j.tcs.2011.12.079</a>."},"project":[{"name":"SFB 901","_id":"1"},{"name":"SFB 901 - Subprojekt A1","_id":"5"},{"_id":"2","name":"SFB 901 - Project Area A"}],"doi":"10.1016/j.tcs.2011.12.079","title":"Tiara: A self-stabilizing deterministic skip list and skip graph","year":"2012","author":[{"last_name":"Clouser","first_name":"Thomas","full_name":"Clouser, Thomas"},{"first_name":"Mikhail","last_name":"Nesterenko","full_name":"Nesterenko, Mikhail"},{"last_name":"Scheideler","first_name":"Christian","full_name":"Scheideler, Christian","id":"20792"}],"date_updated":"2022-01-06T07:02:38Z","file":[{"file_id":"1268","success":1,"content_type":"application/pdf","file_name":"574-tiara.pdf","access_level":"closed","file_size":315843,"relation":"main_file","date_updated":"2018-03-15T09:09:29Z","date_created":"2018-03-15T09:09:29Z","creator":"florida"}],"date_created":"2017-10-17T12:42:44Z","type":"journal_article","department":[{"_id":"79"}],"publication":"Theoretical Computer Science","abstract":[{"text":"We present Tiara — a self-stabilizing peer-to-peer network maintenance algorithm. Tiara is truly deterministic which allows it to achieve exact performance bounds. Tiara allows logarithmic searches and topology updates. It is based on a novel sparse 0-1 skip list. We then describe its extension to a ringed structure and to a skip-graph.Key words: Peer-to-peer networks, overlay networks, self-stabilization.","lang":"eng"}]},{"type":"mastersthesis","date_created":"2017-10-17T12:42:44Z","project":[{"_id":"1","name":"SFB 901"},{"name":"SFB 901 - Subprojekt A1","_id":"5"},{"_id":"2","name":"SFB 901 - Project Area A"}],"citation":{"ama":"Bremer L. <i>Symbiotic Coupling of Peer-to-Peer and Cloud Systems</i>. Universität Paderborn; 2012.","bibtex":"@book{Bremer_2012, title={Symbiotic Coupling of Peer-to-Peer and Cloud Systems}, publisher={Universität Paderborn}, author={Bremer, Lars}, year={2012} }","mla":"Bremer, Lars. <i>Symbiotic Coupling of Peer-to-Peer and Cloud Systems</i>. Universität Paderborn, 2012.","short":"L. Bremer, Symbiotic Coupling of Peer-to-Peer and Cloud Systems, Universität Paderborn, 2012.","chicago":"Bremer, Lars. <i>Symbiotic Coupling of Peer-to-Peer and Cloud Systems</i>. Universität Paderborn, 2012.","apa":"Bremer, L. (2012). <i>Symbiotic Coupling of Peer-to-Peer and Cloud Systems</i>. Universität Paderborn.","ieee":"L. Bremer, <i>Symbiotic Coupling of Peer-to-Peer and Cloud Systems</i>. Universität Paderborn, 2012."},"user_id":"15504","_id":"575","publisher":"Universität Paderborn","date_updated":"2022-01-06T07:02:38Z","author":[{"full_name":"Bremer, Lars","last_name":"Bremer","first_name":"Lars"}],"status":"public","title":"Symbiotic Coupling of Peer-to-Peer and Cloud Systems","year":"2012"},{"type":"conference_editor","department":[{"_id":"79"}],"file":[{"date_created":"2018-03-21T13:09:19Z","creator":"florida","file_id":"1569","success":1,"content_type":"application/pdf","file_name":"577-SSS2012Richa-Scheideler.pdf","access_level":"closed","file_size":169564,"relation":"main_file","date_updated":"2018-03-21T13:09:19Z"}],"date_created":"2017-10-17T12:42:44Z","abstract":[{"lang":"eng","text":"SSS is an international forum for researchers and practitioners in the design and development of distributed systems with self-properties: (classical) self-stabilizing, self-configuring, self-organizing, self-managing, self-repairing, self-healing, self-optimizing, self-adaptive, and self-protecting. Research in distributed systems is now at a crucialpoint in its evolution, marked by the importance of dynamic systems such as peer-to-peer networks, large-scale wireless sensor networks, mobile ad hoc networks, cloud computing, robotic networks, etc. Moreover, new applications such as grid and web services, banking and e-commerce, e-health and robotics, aerospace and avionics, automotive, industrial process control, etc. have joined the traditional applications of distributed systems. The theory of self-stabilization has been enriched in the last 30 years by high quality research contributions in the areas of algorithmic techniques, formal methodologies, model theoretic issues, and composition techniques. All these areas are essential to the understanding and maintenance of self-properties in fault-tolerant distributed systems."}],"project":[{"_id":"1","name":"SFB 901"},{"name":"SFB 901 - Subprojekt C1","_id":"13"},{"_id":"4","name":"SFB 901 - Project Area C"}],"file_date_updated":"2018-03-21T13:09:19Z","citation":{"ama":"Richa AW, Scheideler C, eds. <i>Stabilization, Safety, and Security of Distributed Systems</i>.; 2012. doi:<a href=\"https://doi.org/10.1007/978-3-642-33536-5\">10.1007/978-3-642-33536-5</a>","short":"A.W. Richa, C. Scheideler, eds., Stabilization, Safety, and Security of Distributed Systems, 2012.","chicago":"Richa, Andrea W., and Christian Scheideler, eds. <i>Stabilization, Safety, and Security of Distributed Systems</i>, 2012. <a href=\"https://doi.org/10.1007/978-3-642-33536-5\">https://doi.org/10.1007/978-3-642-33536-5</a>.","bibtex":"@book{Richa_Scheideler_2012, title={Stabilization, Safety, and Security of Distributed Systems}, DOI={<a href=\"https://doi.org/10.1007/978-3-642-33536-5\">10.1007/978-3-642-33536-5</a>}, year={2012} }","mla":"Richa, Andrea W., and Christian Scheideler, editors. <i>Stabilization, Safety, and Security of Distributed Systems</i>. 2012, doi:<a href=\"https://doi.org/10.1007/978-3-642-33536-5\">10.1007/978-3-642-33536-5</a>.","apa":"Richa, A. W., &#38; Scheideler, C. (Eds.). (2012). <i>Stabilization, Safety, and Security of Distributed Systems</i>. Presented at the Stabilization, Safety, and Security of Distributed Systems (SSS), Paderborn, Germany. <a href=\"https://doi.org/10.1007/978-3-642-33536-5\">https://doi.org/10.1007/978-3-642-33536-5</a>","ieee":"A. W. Richa and C. Scheideler, Eds., <i>Stabilization, Safety, and Security of Distributed Systems</i>. 2012."},"ddc":["040"],"doi":"10.1007/978-3-642-33536-5","user_id":"15504","editor":[{"full_name":"Richa, Andrea W.","last_name":"Richa","first_name":"Andrea W."},{"id":"20792","first_name":"Christian","last_name":"Scheideler","full_name":"Scheideler, Christian"}],"_id":"577","date_updated":"2022-01-06T07:02:39Z","has_accepted_license":"1","title":"Stabilization, Safety, and Security of Distributed Systems","year":"2012","status":"public","conference":{"location":"Paderborn, Germany","start_date":"2012-10-01","name":"Stabilization, Safety, and Security of Distributed Systems (SSS)","end_date":"2012-10-04"}}]
