conference paper
Minimum Linear Arrangement of Series-Parallel Graphs
Christian
Scheideler
author 20792
Martina
Eikel
author
Alexander
Setzer
author 11108
79
department
SFB 901
project
SFB 901 - Subprojekt A1
project
SFB 901 - Project Area A
project
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.
https://ris.uni-paderborn.de/download/397/1381/397-WAOA14_01.pdf
application/pdf
2014
Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA)
168--180
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.
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.
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.
@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} }
Scheideler, C., Eikel, M., & 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).
C. Scheideler, M. Eikel, A. Setzer, in: Proceedings of the 12th Workshop on Approximation and Online Algorithms (WAOA), 2014, pp. 168--180.
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.
3972017-10-17T12:42:09Z2022-01-06T07:00:02Z