{"abstract":[{"lang":"eng","text":"We present a factor $14D^2$ approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where $D$ is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time $O(|E|)$ and is very easy to implement. Its divide-and-conquer approach allows for an effective parallelization. Note that a suitable decomposition can also be computed in time $O(|E|\\log{|E|})$ (or even $O(\\log{|E|}\\log^*{|E|})$ on an EREW PRAM using $O(|E|)$ processors). For the proof of the approximation ratio, we use a sophisticated charging method that uses techniques similar to amortized analysis in advanced data structures. On general graphs, the minimum linear arrangement problem is known to be NP-hard. To the best of our knowledge, the minimum linear arrangement problem on series-parallel graphs has not been studied before."}],"_id":"397","date_updated":"2022-01-06T07:00:02Z","ddc":["040"],"title":"Minimum Linear Arrangement of Series-Parallel Graphs","citation":{"mla":"Scheideler, Christian, et al. “Minimum Linear Arrangement of Series-Parallel Graphs.” <i>Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA)</i>, 2014, pp. 168--180.","apa":"Scheideler, C., Eikel, M., &#38; Setzer, A. (2014). Minimum Linear Arrangement of Series-Parallel Graphs. In <i>Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA)</i> (pp. 168--180).","chicago":"Scheideler, Christian, Martina Eikel, and Alexander Setzer. “Minimum Linear Arrangement of Series-Parallel Graphs.” In <i>Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA)</i>, 168--180. LNCS, 2014.","ama":"Scheideler C, Eikel M, Setzer A. Minimum Linear Arrangement of Series-Parallel Graphs. In: <i>Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA)</i>. LNCS. ; 2014:168--180.","bibtex":"@inproceedings{Scheideler_Eikel_Setzer_2014, series={LNCS}, title={Minimum Linear Arrangement of Series-Parallel Graphs}, booktitle={Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA)}, author={Scheideler, Christian and Eikel, Martina and Setzer, Alexander}, year={2014}, pages={168--180}, collection={LNCS} }","ieee":"C. Scheideler, M. Eikel, and A. Setzer, “Minimum Linear Arrangement of Series-Parallel Graphs,” in <i>Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA)</i>, 2014, pp. 168--180.","short":"C. Scheideler, M. Eikel, A. Setzer, in: Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA), 2014, pp. 168--180."},"file_date_updated":"2018-03-20T06:58:44Z","publication":"Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA)","has_accepted_license":"1","author":[{"id":"20792","full_name":"Scheideler, Christian","last_name":"Scheideler","first_name":"Christian"},{"first_name":"Martina","full_name":"Eikel, Martina","last_name":"Eikel"},{"first_name":"Alexander","full_name":"Setzer, Alexander","last_name":"Setzer","id":"11108"}],"status":"public","department":[{"_id":"79"}],"year":"2014","project":[{"_id":"1","name":"SFB 901"},{"name":"SFB 901 - Subprojekt A1","_id":"5"},{"name":"SFB 901 - Project Area A","_id":"2"}],"file":[{"file_size":365818,"relation":"main_file","access_level":"closed","file_name":"397-WAOA14_01.pdf","date_updated":"2018-03-20T06:58:44Z","content_type":"application/pdf","file_id":"1381","creator":"florida","date_created":"2018-03-20T06:58:44Z","success":1}],"date_created":"2017-10-17T12:42:09Z","page":"168--180","type":"conference","user_id":"15504","series_title":"LNCS"}